JavaCard OS

Is TCP is really mandatory for the Java Card 3.0? Is it possible to implement the TCP over the APDU interface? and do we need to implement some kind of proxy in the card?

TCP is mandatory, and APDU is mandatory as well, as you need to be compatible to the Classic Edition. You need to run a server on the card and your communication layer has to process the TCP over IP/UDP/USB packets beforehand.