Hello! So… I would say that I think you can accomplish all of the things you are asking but the how may vary by use case. I’ll link a few articles to start that you may have not run into yet but I think it will be difficult to offer concrete advice just yet. However, perhaps someone else who sees this post and has used the Pay API more extensively will offer some ideas as well
Are you using Wix Bookings? There is an article about how to set up notifications and also how to send yourself a test email so you can see what’s up.
This Velo tutorial may help answer your database question:
Velo Tutorial: Using the Velo Pay API to Collect Payments for Products in a Database Collection
As for your question about notifications, check out the Notifications API and see if you can set up whatever custom notifications you like through there