So,all I need to do is edit bat. file in T-Rex and replace existing address with the one from the Trezor?
Yes, if it is your paying address.
I thought so,but one day when I want to send coins back to Coinbase to sell them,will I have to pay fees for transfer from Trezor to Coinbase?
It will be better to used an address on noncustododial wallet like Trezor for the paying address, transaction fee on such wallets are much lower if compared to exchanges.
Also,I mined 0.03 ETH on Ethermine,I suppose if I change wallet address in T-Rex miner,I won't lose those 0.03 ETH that I'm currently mining?
I am not a miner, but I think you are paid on an address you are given, then nothing will happen to the fund.