How can I add subscription options to the checkout page?
You cannot edit the checkout page at all unless you're a Shopify Plus member
Is it possible to edit the cart and add subscription options to it?
Yeah you can edit the cart, I'm not really sure what you mean by subscription options though. What exactly are you looking to do?
I'm using a "Buy Now" cart icon as my homepage is locked so when my customers click on it, it takes them to the cart where they can choose a subscription option. Once paid, they will be able to access the site.