In order to prepare this, I installed Metamask browser extension and I'm on step to transfer some BNB to it from my Binance account.
Make sure you have changed the network setting on metamask from Ethereum to Binance smart chain (you have to add the Binance smart chain details manually)The BNB you send from Binance must also be the token type on Binance smart chain (BEP20)
1. what's the difference between swapping tokens in Metamask vs. connecting the Metamask wallet to a DEX? Can it work without such connection?
A DEX gives you more options2. assuming my transaction is successful so I have the token in my wallet, how can I swap it to USDT (stable coin) instead of swapping back to BNB? Do I have to add TRC20 network, import USDT contract?
You can't make a cross chain swap, but you can swap or exchange the token for Binance smart chain pegged USDT (USDT BEP20) or BUSD3. what's the best method to send my funds from Metamask back to Binance account? (what coin, what network, etc)
Any of the available USDT options such as (BEP20), ERC20 or TRC20 or even BNB. Just be sure of the network you are using 