So here is my question. Jack of all Trades effects any ability check, that proficiency isn't added to. So what kind of roll is cure wounds for instance. If it isn't an attack or a save it must be an ability check right? If it is an ability check would Jack of all Trades apply?
no. ability checks are d20 rolls. and not even all d20 rolls must be those three things. you can typically identify ability checks because they will say something like "make a(n) <attribute> check" or "you can escape with a(n) <attribute> check". for example, if you want to sneak somewhere, you make a dexterity (stealth) check. note that skill and tool checks are actually just ability checks to which a skill or tool proficiency applies; in that sneaking example, sneaking is a dexterity check that you get to add your proficiency bonus to if you are proficient in stealth.
jack of all trades does apply to some spells, however. dispel magic and counterspell are the ones that stand out, but it also applies to telekinesis. it may apply to others, but i can't think of any off the top of my head (or at least, not in terms of the caster needing an ability check to use the spell... entangle and web among others require ability checks to escape them, for example, so if you're ever stuck in one, remember that).
it also applies to initiative, which you may find useful.