Third-party payment services provider like Stripe

I plan on developing a Shopify app which will play a key role in my website. Flow should go as follows:

  1. User creates an account on my website
  2. User connects his Shopify store
  3. User selects a type of subscription he will work under
  4. User then proceeds to the payment
  5. User starts using my website’s functionality

Am I right that for my Shopify app to be approved and listed on the Shopify App Store, that payment has to be authorized through Shopify Billing API? Does that mean that using Shopify Payments instead of for example Stripe is absolutely necessary there as long as Shopify Payments is available in my location?

Let’s imagine I would want to integrate other e-commerce management systems such as Shopify and only use my website-scale subscription, not new subscription per each new service. Is it even possible?

Does that Shopify restriction also mean that if I wanted a single user to be able to connect more than one Shopify store, there should be a new payment per store?

This is correct - if Shopify Payments is available you’ll need to use this.

a single user to be able to connect more than one Shopify store

If the app is on two stores, it will generate a subscription for both.