How do I change cart and dropwdown menu icons?

[Stefan__]

I'm absolutely new to Shopify. I was trying to figure out how to change them, but eventually I either got the icon disappearing completely, or appearing but too large, with inability to change the size, because only short SVG code with no size indication in it prevents the icon from disappearing, and when the icon appears then it has some black box around it.

Looking at the Youtube guides I noticed that others have icon-empty-cart.liquid while I have icon-empty-cart.svg if that says anything. I'm using Radiant theme.

 For example right now it finally appeared, but it's too large and with black box around it.
Here's the code I currently have in icon-empty-cart and icon-cart files:
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" xml:space="preserve"><path d="M1 199V1h512v512H1V199m138.44-84.955c-4.001 13.023-8.082 26.023-11.976 39.078-2.422 8.122-3.253 8.877-11.9 8.877-21.164 0-42.328.05-63.492-.052-3.347-.016-4.919.48-5.246 4.507-.533 6.576-2.212 13.057-3.345 19.588-1.854 10.685-3.641 21.382-5.485 32.069-1.844 10.682-3.736 21.356-5.583 32.038-1.82 10.526-3.599 21.06-5.416 31.586-1.871 10.842-3.786 21.677-5.646 32.52-1.807 10.531-3.566 21.07-5.352 31.604-1.813 10.695-3.785 21.365-5.409 32.088-1.702 11.242-3.775 22.495-4.41 33.814-.763 13.623-.808 27.359.027 40.973.62 10.107 2.272 20.345 5.045 30.074 2.943 10.324 7.182 14.22 14.71 14.219 153.983-.037 307.965-.032 461.947-.01 4.83 0 8.631-1.902 11.047-5.981 6.336-10.695 8.368-22.718 8.872-34.77.688-16.469.18-32.988.16-49.486-.003-1.48-.055-2.982-.304-4.435-1.526-8.928-3.122-17.844-4.682-26.766-1.923-10.996-3.868-21.989-5.742-32.993-1.794-10.537-3.504-21.087-5.262-31.63-1.757-10.541-3.481-21.088-5.306-31.617-2.183-12.591-4.47-25.163-6.687-37.748a11153.15 11153.15 0 0 1-5.75-32.993c-2.429-14.033-5.109-28.03-7.08-42.127-.545-3.906-1.837-4.553-5.22-4.527-16.164.123-32.33.06-48.494.052-6.153-.003-7.728-1.73-9.543-7.473-5.209-16.48-9.907-33.206-16.462-49.155-6.824-16.605-16.787-31.531-28.62-45.305-11.246-13.088-24.443-23.356-39.56-31.193-14.371-7.45-30.084-11.072-46.084-11.6-11.692-.385-23.66.725-35.167 2.926-28.814 5.513-51.528 21.56-69.602 44.105-11.916 14.865-21.572 31.254-28.983 49.743z"/><path fill="#FFF" d="M139.7 113.742c7.15-18.186 16.807-34.575 28.723-49.44 18.074-22.546 40.788-38.592 69.602-44.105 11.508-2.201 23.475-3.311 35.167-2.926 16 .528 31.713 4.15 46.084 11.6 15.117 7.837 28.314 18.105 39.56 31.193 11.833 13.774 21.796 28.7 28.62 45.305 6.555 15.949 11.253 32.674 16.462 49.155 1.815 5.744 3.39 7.47 9.543 7.473 16.165.009 32.33.071 48.494-.052 3.383-.026 4.675.62 5.22 4.527 1.971 14.097 4.651 28.094 7.08 42.127 1.903 11 3.813 21.999 5.75 32.993 2.216 12.585 4.504 25.157 6.687 37.748 1.825 10.529 3.549 21.076 5.306 31.617 1.758 10.543 3.468 21.093 5.262 31.63 1.874 11.004 3.819 21.997 5.742 32.993 1.56 8.922 3.156 17.838 4.682 26.766.249 1.453.301 2.955.303 4.435.02 16.498.53 33.017-.159 49.487-.504 12.05-2.536 24.074-8.872 34.769-2.416 4.079-6.216 5.981-11.047 5.98-153.982-.02-307.964-.026-461.947.01-7.528.002-11.767-3.894-14.71-14.218-2.773-9.729-4.425-19.967-5.045-30.074-.835-13.614-.79-27.35-.026-40.973.634-11.32 2.707-22.572 4.41-33.814 1.623-10.723 3.595-21.393 5.408-32.088 1.786-10.534 3.545-21.073 5.352-31.603 1.86-10.844 3.775-21.679 5.646-32.52 1.817-10.528 3.596-21.06 5.416-31.587 1.847-10.682 3.74-21.356 5.583-32.038 1.844-10.687 3.631-21.384 5.485-32.069 1.133-6.531 2.812-13.012 3.345-19.588.327-4.027 1.899-4.523 5.246-4.507 21.164.103 42.328.052 63.493.052 8.646 0 9.477-.755 11.9-8.877 3.893-13.055 7.974-26.055 12.235-39.38m312.82 307.27c-.458-.854-1.08-1.66-1.351-2.569-5.459-18.278-11.573-36.397-16.114-54.902-4.802-19.572-8.686-39.42-11.877-59.322-2.837-17.698-4.556-35.605-6.059-53.479-1.243-14.788-1.481-29.662-2.108-44.501-.391-9.25-.659-18.504-1.02-27.754-.16-4.064-2.357-6.287-6.399-6.459-3.16-.134-6.332-.027-9.498-.027H220.108c-7.506 0-9.105 1.634-9.108 9.284-.001 3.5.284 7.028-.063 10.493-.602 5.997-2.326 11.672-8.937 13.57-2.92.837-6.183.555-9.295.635-5.595.143-7.671 2.119-7.694 7.705-.04 9.499.21 19.006-.115 28.494-.139 4.04 1.948 6.162 5.069 6.687 17.234 2.896 29.457 21.249 29.42 38.294-.038 17.299-13.665 35.094-31.248 38.223-21.245 3.78-42.718-9.65-46.387-30.291-3.652-20.545 7.058-41.425 28.197-46.165 3.334-.748 5.097-3.14 5.074-6.771-.062-9.832.024-19.665-.042-29.497-.03-4.334-2.42-6.525-6.711-6.653-1.665-.05-3.333-.007-5-.008-7.581-.003-12.234-3.824-13.208-11.428-.666-5.193-.793-10.46-1.04-15.7-.2-4.253-2.193-6.807-6.54-6.84a2480.01 2480.01 0 0 0-35.996-.002c-4.063.028-6.193 2.341-6.486 6.379-.321 4.42-.803 8.832-.973 13.256-.724 18.835-1.325 37.674-2.048 56.509-.183 4.757-.438 9.53-1.026 14.25-1.89 15.176-3.702 30.369-6.019 45.483-2.377 15.506-4.457 31.138-8.22 46.33-4.74 19.125-10.736 37.962-16.769 56.737-8.03 24.99-19.827 48.106-36.176 68.778-2.166 2.739-1.715 5.089 1.638 6.302 1.775.643 3.779.909 5.679.91 147.321.04 294.643.04 441.965-.008 2.058 0 4.278-.296 6.135-1.109 2.69-1.178 2.961-3.454 1.316-5.843-5.216-7.576-11.157-14.754-15.527-22.787-6.266-11.52-11.395-23.66-17.453-36.204m-264.486-304.39c-4.607 11.597-9.391 23.128-13.758 34.815-2.812 7.525-.4 10.56 7.669 10.56 55.795.003 111.59.002 167.385.002 8.856 0 9.972-1.068 7.605-9.642-6.269-22.71-15.819-44.013-31.27-61.93-13.846-16.054-31.128-26.337-53.016-28.68-13.127-1.404-25.105 1.016-36.82 5.959-22.446 9.47-36.449 27.401-47.795 48.916m285.93 148.152c-.258-.428-.677-.83-.752-1.288-1.76-10.877-3.41-21.772-5.23-32.638-2.942-17.555-5.881-35.111-9.082-52.62-.692-3.787-3.414-6.225-7.65-6.228-6.831-.004-13.664-.057-20.495.02-4.268.048-6.755 2.26-6.7 6.613.033 2.586.795 5.155.915 7.746 1.05 22.583 1.95 45.173 3.07 67.752.423 8.512.998 17.04 2.052 25.491 1.345 10.779 3.115 21.51 4.939 32.222 2.251 13.225 3.977 26.605 7.316 39.561 4.918 19.085 10.387 38.088 16.864 56.694 7.082 20.343 16.895 39.538 29.052 57.405.956 1.405 3.673 2.452 5.383 2.227 1.273-.167 3.009-2.561 3.212-4.135.964-7.458 1.702-14.963 2.096-22.474.943-17.974-.749-35.785-3.97-53.46-1.913-10.49-4.07-20.936-5.916-31.437-1.822-10.371-3.347-20.794-5.08-31.18-1.783-10.695-3.684-21.37-5.487-32.061a1871.7 1871.7 0 0 1-4.537-28.21M50.997 204.35c-.324.913-.794 1.802-.95 2.743-2.706 16.293-5.36 32.594-8.053 48.89-2.323 14.054-4.574 28.122-7.055 42.15-3.208 18.143-6.816 36.217-9.875 54.384a2355.524 2355.524 0 0 0-9.027 58.134c-2.536 17.755-1.025 35.513 1.112 53.198.181 1.498 2.045 3.559 3.48 3.909 1.256.306 3.53-1.047 4.465-2.32 13.734-18.697 23.582-39.517 30.709-61.387 7.25-22.25 13.292-44.935 18.861-67.675 3.418-13.957 5.224-28.336 7.244-42.598 1.466-10.346 2.221-20.8 3.074-31.224 1.431-17.493 2.819-34.99 3.966-52.503.626-9.56.675-19.155 1.067-28.73.26-6.354-1.543-9.169-6.583-9.281-6.994-.156-13.995-.103-20.99-.015-3.952.05-6.622 2.454-7.323 6.016-1.656 8.416-2.78 16.938-4.122 26.31M149.503 162c9.307.027 10.657 1.188 13.891-10.472 3.325-11.984 7.915-23.672 12.691-35.183 4.773-11.504 11.545-21.894 19.495-31.59 10.312-12.577 22.37-22.447 37.883-27.9 13.535-4.76 27.17-6.611 41.628-5.108 10.97 1.141 21.516 3.528 31.014 8.47 19.632 10.213 33.431 26.53 43.901 45.8a197.468 197.468 0 0 1 17.52 44.162c3.526 13.414 2.486 11.703 16.62 11.808 9.124.068 10.713-2.168 8.327-11.062-4.958-18.489-11.549-36.287-20.983-53.039-9.332-16.57-20.324-31.608-34.967-44.022-18.894-16.018-40.586-24.905-65.085-26.753-12.432-.938-24.739.898-36.712 4.577-25.976 7.983-46.463 23.876-62.145 45.497-16.841 23.22-28.32 49.183-34.582 77.306-1.096 4.92.623 7.227 5.564 7.494 1.66.09 3.33.015 5.94.015m16.234 100.023c-8.562 5.244-13.594 13.044-14.627 22.818-1.918 18.152 20.408 37.185 38.138 29.373 10.614-4.676 17.41-12.097 19.498-22.82 2.157-11.08-2.695-20.59-11.644-27.288-9.519-7.126-19.874-9.013-31.365-2.083M160 184.472c0 1.5-.041 3 .008 4.5.155 4.724 2.21 6.95 6.856 7 9.164.096 18.33.064 27.496.011 4.063-.023 6.413-2.175 6.601-6.237.177-3.825.158-7.669.005-11.496-.152-3.801-2.287-6.145-6.11-6.202a967.452 967.452 0 0 0-28.496-.003c-4.028.058-6.224 2.394-6.351 6.488-.052 1.665-.009 3.332-.009 5.939z"/><path d="M452.742 421.347c5.836 12.21 10.965 24.35 17.231 35.87 4.37 8.033 10.311 15.21 15.527 22.787 1.645 2.39 1.375 4.665-1.316 5.843-1.857.813-4.077 1.108-6.135 1.109-147.322.048-294.644.047-441.965.007-1.9 0-3.904-.266-5.679-.909-3.353-1.213-3.804-3.563-1.638-6.302 16.35-20.672 28.146-43.788 36.176-68.778 6.033-18.775 12.03-37.612 16.768-56.737 3.764-15.192 5.844-30.824 8.221-46.33 2.317-15.114 4.128-30.307 6.02-45.483.587-4.72.842-9.493 1.025-14.25.723-18.835 1.324-37.674 2.048-56.509.17-4.424.652-8.837.973-13.256.293-4.038 2.423-6.351 6.486-6.379a2480.01 2480.01 0 0 1 35.996.002c4.347.033 6.34 2.587 6.54 6.84.247 5.24.374 10.507 1.04 15.7.974 7.604 5.627 11.425 13.208 11.428 1.667 0 3.335-.041 5 .008 4.29.128 6.681 2.32 6.71 6.653.067 9.832-.019 19.665.043 29.497.023 3.63-1.74 6.023-5.074 6.77-21.14 4.741-31.85 25.621-28.197 46.166 3.669 20.641 25.142 34.071 46.387 30.29 17.583-3.128 31.21-20.923 31.248-38.222.037-17.045-12.186-35.398-29.42-38.294-3.121-.525-5.208-2.646-5.07-6.687.326-9.488.077-18.995.116-28.494.023-5.586 2.099-7.562 7.694-7.705 3.112-.08 6.375.202 9.295-.636 6.61-1.897 8.335-7.572 8.937-13.57.347-3.464.062-6.992.063-10.492.003-7.65 1.602-9.283 9.108-9.283 59.329-.002 118.657-.001 177.986-.001 3.166 0 6.337-.107 9.498.027 4.042.172 6.24 2.395 6.399 6.46.361 9.25.629 18.504 1.02 27.753.627 14.839.865 29.713 2.108 44.501 1.503 17.874 3.222 35.78 6.06 53.479 3.19 19.902 7.074 39.75 11.876 59.322 4.54 18.505 10.655 36.624 16.114 54.902.271.91.893 1.715 1.573 2.903zM188.264 116.314c11.116-21.206 25.12-39.137 47.565-48.607 11.715-4.943 23.693-7.363 36.82-5.958 21.888 2.342 39.17 12.625 53.015 28.68 15.452 17.916 25.002 39.219 31.27 61.929 2.368 8.574 1.252 9.642-7.604 9.642-55.795 0-111.59.001-167.385-.001-8.07 0-10.48-3.036-7.669-10.56 4.367-11.688 9.15-23.219 13.988-35.125z"/><path d="M473.98 265.22a2867.001 2867.001 0 0 0 4.52 27.765c1.804 10.691 3.705 21.366 5.488 32.06 1.733 10.387 3.258 20.81 5.08 31.18 1.845 10.502 4.003 20.948 5.916 31.438 3.221 17.675 4.913 35.486 3.97 53.46-.394 7.51-1.132 15.016-2.096 22.474-.203 1.574-1.94 3.968-3.212 4.135-1.71.225-4.427-.822-5.383-2.227-12.157-17.867-21.97-37.062-29.052-57.405-6.477-18.606-11.946-37.61-16.864-56.694-3.34-12.956-5.065-26.336-7.316-39.56-1.824-10.712-3.594-21.444-4.939-32.223-1.054-8.452-1.63-16.979-2.052-25.491-1.12-22.58-2.02-45.169-3.07-67.752-.12-2.59-.882-5.16-.915-7.746-.055-4.354 2.432-6.565 6.7-6.613 6.831-.077 13.664-.024 20.496-.02 4.235.003 6.957 2.44 7.65 6.229 3.2 17.508 6.139 35.064 9.08 52.619 1.82 10.866 3.47 21.761 5.231 32.638.075.458.494.86.769 1.733zM50.999 203.904c1.34-8.925 2.464-17.447 4.12-25.863.701-3.562 3.371-5.966 7.322-6.016 6.996-.088 13.997-.141 20.99.015 5.041.112 6.844 2.927 6.584 9.28-.392 9.576-.441 19.172-1.067 28.73-1.147 17.513-2.535 35.011-3.966 52.504-.853 10.424-1.608 20.878-3.074 31.224-2.02 14.262-3.826 28.641-7.244 42.598-5.57 22.74-11.612 45.425-18.861 67.675-7.127 21.87-16.975 42.69-30.71 61.387-.935 1.273-3.208 2.626-4.464 2.32-1.435-.35-3.299-2.41-3.48-3.909-2.137-17.685-3.648-35.443-1.112-53.198a2355.524 2355.524 0 0 1 9.027-58.134c3.06-18.167 6.667-36.241 9.875-54.384 2.48-14.028 4.732-28.096 7.055-42.15 2.694-16.296 5.347-32.597 8.053-48.89.156-.94.626-1.83.952-3.189zM149.03 162c-2.137 0-3.806.075-5.467-.015-4.941-.267-6.66-2.574-5.564-7.494 6.261-28.123 17.74-54.086 34.582-77.306 15.682-21.621 36.17-37.514 62.145-45.497 11.973-3.68 24.28-5.515 36.712-4.577 24.499 1.848 46.19 10.735 65.085 26.753 14.643 12.414 25.635 27.451 34.967 44.022 9.434 16.752 16.025 34.55 20.983 53.04 2.386 8.893.797 11.13-8.328 11.061-14.133-.105-13.093 1.606-16.62-11.808a197.468 197.468 0 0 0-17.519-44.161c-10.47-19.27-24.27-35.588-43.9-45.802-9.5-4.941-20.045-7.328-31.015-8.469-14.458-1.503-28.093.348-41.628 5.107-15.513 5.454-27.571 15.324-37.883 27.9-7.95 9.697-14.722 20.087-19.495 31.591-4.776 11.511-9.366 23.199-12.69 35.183-3.235 11.66-4.585 10.499-14.364 10.472zM166.117 261.989c11.111-6.896 21.466-5.009 30.985 2.117 8.949 6.699 13.8 16.208 11.644 27.287-2.087 10.724-8.884 18.145-19.498 22.821-17.73 7.812-40.056-11.221-38.138-29.373 1.033-9.774 6.065-17.574 15.007-22.852M177.567 292c3.83 0 7.669-.15 11.49.042 3.919.198 4.89-2.42 4.822-5.28-.063-2.66-1.185-4.964-4.804-4.82-5.487.22-10.994.202-16.483.007-3.684-.13-5.837.283-5.764 5.003.07 4.544 2.266 5.166 5.77 5.055 1.331-.042 2.665-.007 4.97-.007zM160 184.002c0-2.137-.043-3.804.009-5.47.127-4.093 2.323-6.429 6.351-6.487 9.497-.138 19-.14 28.496.003 3.823.057 5.958 2.4 6.11 6.202.153 3.827.172 7.671-.005 11.496-.188 4.062-2.538 6.214-6.6 6.237-9.166.053-18.333.085-27.497-.012-4.646-.049-6.701-2.275-6.856-7-.05-1.498-.008-3-.008-4.97z"/><path fill="#FFF" d="M177.081 292c-1.818 0-3.152-.035-4.483.007-3.504.111-5.7-.51-5.77-5.055-.073-4.72 2.08-5.133 5.764-5.003 5.489.195 10.996.213 16.483-.006 3.62-.145 4.741 2.158 4.804 4.82.068 2.86-.903 5.477-4.823 5.279-3.82-.193-7.658-.042-11.975-.042z"/></svg>

[Stefan__]

I want it to be smalle to fit with the design and for the black box in the background of icon to disappear. And I need a working guide on how to change the menu icon next, because to achieve this cart icon I had to redo the code over 50 so I spent over 2h on it..
I guess if I use the same method I will face the same issue.