Hey @tianhong - this is an interesting idea, thanks for getting in touch! For your first question - there's not a specific API that would allow you to do this, but you could use our POS Link functionality for this. POS link allows you to embed a link into the POS app that could redirect to a page within the merchant's admin based on information you could pull through App Bridge.
App Bridge would allow you to fetch the product information from a user's POS cart. My thinking is that you would need to build a bit of a callback process within your app to store the data that's fetched. Then, you could redirect the user to the right page in their admin based on the myshopify.com domain structure.
It is a bit of a complex workaround for sure but I have seen other developers use App Bridge/POS links to offer similar functionality. In the past, I've seen it mainly used for invoice printing.
When it comes to domain customization, my understanding is that as long as you use the merchant's full myshopify.com URL, it should redirect the user properly. You would need to know the specific store you would want to redirect to within the admin. Since you'd be dealing with a specific POS, it would be assigned to a specific myshopify.com domain/shop, so custom domains shouldn't be an issue here.
The only other thing to be aware of is our new unified domain structure - which could impact the way you create URL redirects. More info on that here. Hope this helps - let us know if we can clarify anything on our end!