I'm mainly asking this for Disgaea: Afternoon of Darkness, given I have enough Mana to reincarnate a character into 4 different types of Mages (Green, Blue, Red, Star), a Cleric and then a Warrior, would the Warrior have all the spells learned from the previous classes?
Yes, spells are kept after reincarnating (it may be that you need to have some minimum of skill experience on the spell to keep it), but they lose a certain amount of skill experience. So you can get any spell on any class, which is also the only way to get the Tera spells on Prism/Galaxy Mages/Skulls.
The skill experience lost depends on how much mana you spend reincarnating, a Genius reincarnation will only lose 5%. As the character will lose any excess mana they still have after reincarnating you should use the best one you can afford.
Yes, unless your skill level drops below a certain percent after reincarnation (below level 1 I believe). A skill you've never once used will (if I recall) be unlearned even using Genius reincarnation, so make sure you have a little bit of skill experience in everything you want to keep, and always use the best reincarnation option possible; Genius if at all possible.