First, I have no idea how you abuse a water heater. I also have no idea how they got rock solid calcium deposits all over the inside of the dishwasher when the water isn't hard or soft (and after chiseling the big stuff off, it's been gradually coming off with regular, normal use). And I similarly have no idea why they used a zip tie to attach the tub faucet to a pipe in the wall. I can continue with the weird/wrong stuff. So I wouldn't put anything past the previous owners, or their children.
Anyway, there is indeed a backflow preventer valve on the water line here, so I do need an expansion tank. Given that the water heater is 8 years old and it's cheaper to install an expansion tank at the same time as replacing the water heater, I think that will be the way to go. I'll go for the volume discount by asking them to take care of the rest of my plumbing list at the same time (I've done several items myself, but these ones I'm not touching). It'll be expensive, but not as bad as an emergency bill.