How to test shopify public app(unlisted) in a live shopify store?

I have developed a Shopify public app and there are some things that I need to test before submitting my app. They are as follows:

1 - If the store uses a custom domain instead of store-name.myshopify.com (generated default by Shopify) as the primary domain of the store then which domain does Shopify return in their return response after OAuth Installation? Custom or Desfault? If a custom domain is returned to us, can we use this custom domain to call Storefront API for that store?

2 - Does Shopify return email used by Shopify Store to access their Shopify account after OAuth Installation?

3 - How to test subscription of a newly developed public app in live Shopify store (Not development store)?