So I started Morrowind up again. I remember that whatever you use/do gives you more points towards that skill or whatnot. I forgot if quests give you XP points. Like meeting a woman on the road and she asks you to take her somewhere. Will doing that quest give me any points or are they completely useless?f

Nope, quests don't give XP.

Only Skill increases count towards your experience.
But doing Quests (even random ones) can sometimes give you Reputation points, which makes people like you more.