There is actually a potential coding solution that another member wrote about here that provides the code necessary to center the logo on the supply theme. With that said, be sure to duplicate your theme first, just in case any issues arise, you still have your original theme before the edits.
As far as not seeing your products, have you added any sections to the homepage to display the products? A featured collection, collection list, or featured product are all sections you can use to showcase your products on the homepage.
If there is anything else I can help you with, please let me know.