Is it smart to put Electrum on a thumb drive, if even possible?
I can't think of a reason this would be better. But it's possible to do.This sounds confusing to me: have things changed these last years? The 15.... key is my public address right? That should not change when I make a transaction is it? Maybe I was never aware how a transaction really took place.
How can I check this in Electrum?
15xxx sounds like your Bitcoin address indeed.How can I check this in Electrum?
Change didn't change
If you just use a wallet, the wallet takes care of your change. If you sweep the funds into your Electrum, your new wallet should take care of it again. But if you import it into a new wallet, it depends on the wallet how it handles it.There are of course sites that can explain it much better than I do, like this one (although a bit outdated): Five Ways to Lose Money with Bitcoin Change Addresses.