All of our SDK’s for custom storefronts are built upon the Storefront API. This includes our Mobile Buy SDKs that help you get up and running faster. Otherwise, you have the Admin APIs which are geared towards more internal admin events/managing data and the Checkout API for sales channels.
In general, yes through the APIs you can handle user logins, inventory, and coupons. For a more Shopping Cart experience however, you will want to check out the Mobile Buy SDKs