Yes Accuracy, Crit, Vit are always applicable stats when it comes to food. In terms of magic and physical accuracy, this game doesn't have such differentiation, however a mage has an easier time hitting enemies, so they tend to have a lower Accuracy requirement than melee DPS. The more class specific stats are Skill and Spell Speed - however in most cases you generally avoid these food.

There's no skill levels. Certain classes gain Traits that boost the use of skills while in certain classes/jobs - for example, traited Blood for Blood means that Lancers/Dragoons gain +25% damage from Blood for Blood, compared to an Archer/Bard or a Pugilist/Monk who cross-class Blood for Blood only gaining +10% damage instead.