Photos often look duller on screen than the scene did in person. A modest adjustment usually closes that gap.
Flat photos usually lack separation between light and dark, not colour. Raising contrast often makes an image look more colourful than raising saturation does, and it looks natural rather than processed.
Skin is where oversaturation gets caught. Landscapes tolerate a lot of extra colour, faces do not, and a portrait pushed too far goes orange in a way everyone notices and nobody can name.
Judge it away from the sliders. Move the adjustment, look at something else for a moment, then look back. Eyes adapt quickly and it is easy to keep pushing past the point where it stopped looking good.
Usually too much saturation. Try backing it off and raising contrast instead.
Yes, apply the same settings across a batch.
No.