Leaking Second Floor Bathroom
You will be able to remove the tub without tearing into any walls or ceilings. The overflow ties into the drain at some point. This is a typical setup (see below).
Once you remove the 2 screws holding the overflow in place and then the drain basket, the drain is now separate from the tub. If you are removing a cast iron tub, the only real way you're going to get it out is with a sledge hammer and bust it into pieces (wear safety glasses and gloves!!!).
I cannot help you with the drain repair question. That's why I use a plumber! I'd assume if you are replacing the tub, this is a non issue. However, if the tub is staying, I'd expect a hole (or 2) will be needed somewhere to access the overflow/drain for repairs. Don't be afraid of that. Plumbers fix pipes behind walls all the time. Drywall can be repaired!
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