Since Ethereum forked, is the testnet forked too or only the main net? Is there a common testnet for forked Ethereum (ETH) and Ethereum classic (ETC), or a testnet for each one?
Morden is the public testnet for the Ethereum protocol. It's always had testnet Ether (ETHT or ETT if one wants to give it a symbol?). Unless the ETC blockchain changes its protocol (for example removing or adding EVM opcodes), all ETC development can be tested on Morden.
The hardfork between ETH and ETC did not change anything about the Ethereum protocol.