So,all I need to do is edit bat. file in T-Rex and replace existing address with the one from the Trezor?
Probaly yes, but I never used that miner and I can't say anything more.
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?
What kind of question is that?
You need to pay fees for sending coins from your own wallet, so make up your mind what you want to do, sell or hold coins.
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?
You are not going to lose anything if you do everything correctly, but you may lose everything if you make some mistake.