1st - It looks like you have no choice but to repair the roof around the valley.
2nd - Shingles do not have to be removed all the way to the ridge, but you need to identify the leak source before you decide how much roof needs to be removed.
3rd - Yes, shingles can be re-used if not damaged during removal, but depending on how long they’ve been in place this could be tricky, especially if you aren’t a roofer. My one suggestion is to remove the shingles with a shingle-bar in the early morning before the sun has started to heat up the shingles. Still, you will probably loose/damage some of the shingles regardless.
4th - I’d be curious to know what type of material other than shingles are in the valley.
5th - Yes, you would be well advised to sand before adding more mud to your ceiling, but it doesn’t have to be a perfect finished-sanding. It just needs to be smooth enough to allow you to add another application of mud. Are these just skim coat applications? If you are using the mud as filler, be sure to apply a tape or mesh, and understand the thicker the application the more apt it is to shrink and crack.