I'd like some advice on ceiling repair in my bathroom, specifically the area above the tub.

When looking facing the side of the tub, the ceiling comes down and then in, forming a lower ceiling like area the width of the tub. This means that there is a vertical section from the "Ceiling" of the tub to the actual bathroom ceiling.

Where the vertical portion meets the actual ceiling cracks / holes have appeared in what appears to be dry wall. In addition, the "ceiling" above the tub is starting to show small lined cracks, it looks as though there is a main centre portion of drywall for the ceiling, and around the sides about 1/2 - 1 inch border, and it's the space between this border and the ceiling where the fine line cracks are appearing

The advice I'm looking for is how best to repair both of these issues.

My first thought was to strip the paint away, polyfilla it, sand it down, then prime and paint. I'm not convinced by that and am thinking that perhaps drywall mesh tape / hole patch kit might be a better approach, the thinking being, remove the old paint, put the tape or patch square over the holes, apply something (drywall compound / plaster?) to fill over it, then sand, prime and paint. This would, I think be able to be done to both areas that need repair.

So, does this sound right, if not, what to do, and what to use?

One problem is this is our only bath / shower, so I need to make sure whatever I do is pretty quick drying / setting, as we cannot really be without a bath / shower for too long.

Any suggestions or advice greatly appreciated.