How to integrate 0-conf BCH payments into a web app?
You can host your own Bitcore Web services Bitcore

You can do things like as follows.


User present QR with the random address using this library Bitcore Library
User sends payment using wallet.
Website will be listening to transaction broadcasted by customer wallet.


Here is the resource for a payment protocol read it thorough you will get an idea. Bitcore Pay Pro

Talking about 0-conf: Once a transaction is sent, it is broadcasted immediately even if the next block has a few minutes before its found. If you as a merchant running  a node has capability to verify the transactions.

You can host your own BWS. No need to rely on 3rd party.

For more please refer to bws docs.