TronWallet supports the BTT token. This is because BTT is on the Tron Network. So you are safe to hold and recieve the BTT token in your wallet. You can use your TronWallet address (tab Recieve) to send and recieve BTT.
Every month BitTorrent airdrops to TRX holders some BTT. To qualify for BTT airdrop you need to hold TRX in your wallet. It doesn't matter if they are frozen or unfrozen.
When you didn't have recieved the BTT, but you have hold TRX in your wallet, then you can contact BitTorrent on https://t.me/BTTBitTorrent to ask why you didn't recieved the BTT airdorp. This is something TronWallet doesn't handles.
When you want to send BTT token to Binance you must send round numbers to Binance and not with decimals. This is because Binance only handles transactions with round numbers.