Feel free to post any pictures of the tub drain setup. That way we can be sure if it’s going to be a problem with the new tub. As long as a joist isn’t blocking the drain and you have some access it should be okay.
Adding 2×8 or 2×10 wood to the stud walls will be good for the hand rails. Either toenail or screw them with 3″ deck screws. It’s best to get all the walls open in the tub surround, install the tub, then add the blocking. That way you can be sure it’s at the right height for the person using it.