Drywall – How to repair drywall seams that have developed cracks

Personally, I would just build a rectangle out of 2x4s slightly smaller than the hole, lower it into the hole flush with the existing framing, then screw it to the existing framing. That will give you a nice surface to attach your new drywall to. Depending on the size of the hole, you might want a cross member in the box as well so your drywall isn't spanning too big of a hole unsupported.

As for cutting back the existing drywall - I wouldn't bother with that for a couple reasons:

First, you're likely to run into issues with the nails or screws that were used to originally attach the drywall to that framing. If you cut around those, then the old drywall isn't going to have a very secure connection to the framing unless it was glued. And if it was glued, then you have the problem of the glue residue getting in the way of the new piece you want to put on.

Second, the damaged areas of the drywall are well within the areas that you'll need to mud over anyways - figure on mudding out at least 6-12 inches on either side of the joint. So you're really not saving yourself any work by cleaning that up.

First, everything woodchips told you in his answer is absolutely correct, and you should follow his advise about solving the cause of the excessive moisture. Your fan should run for 5 to 10 minutes after using the shower to clear the moisture.

With that said, let's examine the paint problem. I think there are a few factors causing the paint finish to fail. First reason is that moisture is obviously penetrating the paint layer and causing the paint to separate from the wall board, thus peeling or bubbling occurs. This is usually caused by a lack of a proper sealing/primer coat on the wall board. Today, we would use a moisture resistant drywall or mildew/mold proof paperless drywall, but even that would have to be properly sealed to prevent a finish paint failure. The primer has two functions. The primer seals the surface of the drywall to prevent moisture from being absorbed, and secondly creates a strong bonding layer for the paint to adhere to.

In your case, I suspect a couple of things happened. First, the wallboard was not primed properly and most likely a very cheap grade of paint was used directly on the wallboard and mud joints. (thus the rust spots showing through from the fasteners)

Follow woodchips advise and remove the problem areas. If some patching of damaged drywall surface is required, use a setting type drywall compound rather than general purpose compound. Setting type is less susceptible to moisture decay than regular compound. Vinyl spackle can also be used if the spots are small. The next step would be to properly prime the entire ceiling. I would highly recommend using an alcohol based pigmented shellac such as Bin's Bullseye primer. This product will seal the surface and block any moisture stains from bleeding though again. If the staining is very dark or wide spread, two coats of Bullseye would be a good idea. Gently buff sand and remove any dust from the freshly primed surface before painting. When painting, use a good grade of mildew resistant paint. I would use a satin or flat finish enamel instead of common flat ceiling paint. An enamel will give you a much more durable and moisture resistant finish. It will also bond very strongly to the primer.

Side note: Be sure the fan is vented to the out of doors. I have seen them vented directly into the attic space. Excessive moisture above a ceiling, especially around a cold soffit can cause moisture to migrate down through the ceilings close to an outside wall. This usually causes finish failures along the ceilings on an outside wall. Likewise, if a soffit area is very cold, moisture will condense on the interior ceiling surface along the outside wall from the inside and cause staining and finish failure.