Hey man, don't really get what you're trying to ask, but we have a guide on Shopify login, hope it helps!
this is a screen shot of a customer who is logged in, looks the same as when logged out (person icon); on the amazon .com website for example, when I am logged in it says 'welcome barb', it might not be that big of deal to know if one is logged in by looking in the corner, just seems many random accounts I have here and there you can tell if logged in already.
in creating a customer account, this is all the farther one can get, clicking the 'add a new address' doesn't go anywhere. I am assuming if a customer is creating a login page on my website, they would be prompted to complete a profile with their name, phone number, address, etc. Or perhaps adding profile details begins only if when placing an order first and then creating a login account upon the completion of the order process?
Yes you can edit all of this in your theme files.
Online Store > Themes > Actions > Edit Code.
Then look in the Templates section, you'll see files like customers/account.liquid, customers/addresses.liquid, etc.
Open those and make the changes you'd like.
The Customer liquid object docs will help.
Make sure you make the edits on a backup theme in case your code is not perfect. If you're not familiar editing themes, here's a guide I wrote: https://speedboostr.com/how-to-safely-edit-your-shopify-theme.
If you'd like your tasks done for you let me know. My team and I (speedboostr.com/about) work on Shopify sites every day.