I had a leak in the roof above my bathroom. I had a contractor investigate. He looked at the roof carefully, and he examined the ceiling with an infrared scanner while it was actually leaking. He explained that the leak was caused by runoff from the upper roof, running across this lower not very steep one, and the water was pooling in the keys of the shingles and finding nail holes. He told me to get a downspout extension to route the upper roof's runoff into the gutter, which I have done, so I feel hopeful there will be no more leak.
However, my bathroom ceiling was damaged by the leak and at least part of it needs replacing. I have attached a picture, showing that the leak came through the fan and to the side of the fan (circled areas).
You can see there is mold in the peeling paint. There is a smaller hole where my husband's thumb easily poked through when it was really soaked.
Do I need to replace the fan as part of repairing the ceiling? Should I assume there is mold in it, but even if so, could I clean it out?
What is the best way to replace the ceiling? I've never replaced a wall or a ceiling, though I've done a lot of spackling and painting. My husband and I both do a lot of small repairs, too, so I think we can do it. I would welcome detailed instructions or pro tips.