#2: No. Just… No.
I have a fridge like this, and I know with 100% confidence that this drawer can be removed and sanitized, but there is no way you could convince me to brine a turkey this way. Unless there is nothing else in this fridge, I’d feel like everything was contaminated.

There is plenty of space for a large pot that will fit a turkey right on top of that drawer, and you won’t even have to go nuclear on your fridge when it’s over. Now, methods aside, brining is definitely the way to go. It helps break down the protein strands and provides a more tender meat for the main course. Just keep it sanitary!