Yes, many exchanges are offering a 0 withdrawal fee when transferring TRC-20 USDT even, binance is offering the same. This feature is excellent in my opinion because I remember during the early days I had to pay 5 USDT as the withdrawal fees (ERC20 one).
Yes, but some exchange still charge $1 fee for USDT-TRC20 withdraw. I hope Binance and other exchange will keep this fee for later. But the transaction speed of the TRC20 network now seems to be slowing down, as every withdrawal of my USDT has to wait 5 to 10 minutes, while it used to be less than 1 minute.