I have a bathroom when there is foul sewer smell whenever anybody takes a shower. I have also noticed that the ceiling below is showing some water damage. The masking tape is swelled up so I am thinking there is a leak. The drains were initially slow and I cleaned the tub drain valve. Will I have to cut a hole in the ceiling to repair the tub leak. I also wanted to replace this tub - is this a good time to do it and get all the problems taken care of at once?

Not an expert, at all!:)
But had the same issue, and it was simply a seal gone in the trap. Once I replaced the inexpensive part, the ceiling began to dry out and no issues since.
Maybe nothing to do with it and you might have checked it already, but I thought it worth a mention

p.s. the smell was the floor below he bath because it was so wet:)

Is your ceiling drywall? If so it MUST be removed because mold will have already started growing. Once the ceiling is down you'll have a better shot at seeing what leaking. Could be the drain but could also be the mixing valve or riser to the shower head