Does it? It seems it doesn't send any notifications but just displays a notification body so I can debug my signature verification algorithm. Can you double check that it actually fires an HTTP request?
3. currently the system does not retry payment notification if it fails. I am working on that right now. We do have https.
How it is supposed to work? I get one callback per transaction with seemingly random confirmations count. Will it fire after every confirmation or just once after 6 confirmations?
5. can you give me a use case why you will want this?
Any case of repeated transactions. E.g. a casino - for a user its convenient to have an address in his bitcoin address book and use it every time when he buys more chips. E.g. a web hosting service - for a user it is much easier just to pay 1 BTC to a fixed address every 1st day of the month than to log in to his account and request a new address every time. In general, there are cases where only total transferred amount is important but there's no need to differentiate individual transactions. At least btcex.com and bitcoin-central.net use this model for adding bitcoins to trading accounts.
6. I am open for any suggestions on this
One possible solution is just use your certificate as a client HTTPS certificate to authenticate you.