It depends where you are, but in general, everybody has to pay taxes.
In most places, you have to pay income tax when your income is over a certain level. You may also be obligated to collect and pay sales tax.
This is the sort of thing you should figure out before you start running a business. Also be aware that the Shopify terms of service (the VERY FIRST THING - section 1, item 1) forbid use of the service by minors.
Leon here from the Shopify Support Team.
What Matthew has said is correct, the Shopify Terms of Service do require all merchants be over 18 years of age. The best option to keep your store open right now would be to have a parent or guardian that can take ownership of your site until you're 18.
As for taxation, the laws vary depending on your location, so it's best to contact your local government to find the registration requirements as they relate to you.
Sales Tax collection on Shopify has been made easy - enter your zip code (if in the USA) and our system will automatically determine the tax rate and how much to tax customers based on their location and yours. When it comes time to submit those taxes to your local government, there is a simple tax report available in Reports > Finances Summary. More on Taxes in Shopify HERE.