"Does it matter if I'm using btc to buy instead of tether?"

Every time you change coins you pay a fee. Good idea to just use whatever coin you have at the point you want to buy if you can choose one or the other.

"Is it better to own crypto in tether, since it is a stablecoin?"

If crypto is losing value, it's good to have stablecoin. If crypto is gaining value, it's good to have crypto. If you're not sure what's happening or if you want a break then stablecoin is a good idea.

"What kinds of issues can I expect from trying to withdraw everything from Kucoin (like converting it all back to btc and transferring to coinbase) if I suddenly decide to bail?"

Fees that you don't expect. Make sure you get all your wallet addresses correct. Make sure you can keep a record of your earnings for tax purposes.

You're doing the right thing asking questions. Keep learning.