Typically studs are spaced 16" on center but that's a general rule that can change. It's hard to find studs behind tile as you're figured out. Assuming 16" OC you can angle the bar to hit both studs. You can use toggle bolts and they'll probably be strong enough. You need to apply some back pressure as you tighten the screw. In the case of several in the same bracket, you need to apply some pressure and tighten each screw a little at a time. They also make special holders for grab bars. Off hand I can't remember the name but their quite heavy duty and unfortunately rather expensive (although far less expensive than a fall and trip to the hospital).

If the new walls are not bearing walls and the ceiling is firm I would not disturb anything! Why make more work for yourself. The new walls just need to remain upright and stable and screwing them through the top plate to the joists or blocking between joists is fine. Drill hole for wires into top plate,go up in attic, install your J-boxes and drop wires down.

If it's wavy because the plaster is loose and starting to fall down, then screwing it back up with plastic washers on the screws will flatten it out and then you can add your drywall layer or just fix the plaster. If it's wavy because the joists aren't flat, then maybe you'd have to pull down the plaster and lath and sister some new joists next to the old ones to flatten the ceiling and attach the drywall to the new joists. But I'd avoid pulling down the plaster. It's a messy job and a pain in the butt to cart off to the dump. How bad are the ceilings? Are you just used to new houses where everything is flat and right angles? Part of the charm of old houses is the imperfections. If the ceilings aren't actually falling down and they have just always been imperfect, I'd suggest just trying to accept them the way they are.

To all responders - many thanks for the comments and suggestions. Was able to open access door at plumbing end of tub and was able to see steel mesh and clumps of plaster below tub rim on exterior wall but no sign of studs - so I assume that plaster with mesh support is also behind wall tiles. This would explain erratic readings with stud finder. Exterior wall is brick - not sure if stud finder will give reliable readings through brick but will give it a try. If so will give me some general idea where studs might be.