3. NFC Pay tapping - 1 Tap = 1 Pay
Not possible. At least not with one tap. You need 1 tap to request the address and amount to send to, then the wallet signs, and then one more tap to send the signed transaction. The reason 1 Tap = 1 Pay works with credit cards is because it's the equivalent of tapping to give the merchant your private key, and then having them only pull out what they need.
Why to send signed transaction by NFC instead releasing it directly to Bitcoin network by smartphone's Internet connection?
Mycelium already supports this. The idea was to be able to use your phone to pay with bitcoin, using the merchant's connection to the bitcoin network, without the user even needing a data connection (for example if you don't have a data plan, have bad reception, or are traveling outside of your coverage area). This would need NFC for the merchant to send the request, and NFC or bluetooth (though bluetooth isn't typically available in payment terminals) to receive the signed transaction back.