Does Reincarnation allows skills to be passed into other classes

Solution 1:

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.

Solution 2:

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.