The wording "the first ability" is new, but it makes sense in how Magic terminology is constructed. I created a new term called "enspiriting," taking haunt as a template for it. Feel free to change this word to whatever you wish. Along with this, I also recommend changing the name of the ability from vary to something like "enspirit." In any case, a designation word is needed in order to be able to associate which card in exile is tied to which permanent on the battlefield, which becomes especially important with cards like your Soulshift. Note that the last sentence in the ability here is a static ability, which means that it is continually checked and updated based on the current state. So if the enspiriting card changes, so will the permanent's ability that is gained. In the comprehensive rules for vary, it would need to be stated that if a card with no abilities is enspiriting a permanent, then it just grants no abilities. But this is not needed in the reminder on the card.
Interesting to have a counter that can go on any target (permanents or players). Adding "slap" before it feels off to me, especially if it's combined with a numeric value for jinx as well. I think this is most similar to support, which is just one word. I think you could just have "jinx 1" or "jinx 2," since jinx is also a verb. (It also would make it sounds less like you are hitting a Pokémon.)
Updated reminder: "Jinx 1 (Put a jinx counter on up to one target.)" or, for more than 1, "Jinx 2 (Put a jinx counter on each of up to two targets.)"
I would use it closer to how you do in Novice of Ineptitude, specifically, "torment target opponent," as opposed to how you have it used in Duel of Incompetents. Note that I changed "an opponent" to "target opponent" to better match the reminder that you have. I agree that this should in fact target, since it can deal damage.
For torment, my concern is that you can do a test with 1 torment card, then hold back the rest until you can get a ton of damage in. Also, it benefits you playing with both very low as well as very high cost cards. Maybe play with the idea of only dealing damage if your card is the higher cost? Also, in order to prevent multiple torments to deal the same damage (it feels bad for you if you're getting 0 damage for the whole turn, and feels bad for the opponent if you do a ton of damage with each in a turn), you can either mill the top card instead of just revealing it, or put it on the botton of the deck after reveal. This way, tormenting multiple times in a turn is no longer deterministic, and it becomes a lot more difficult to set up multiple torments to hit for a lot. I wouldn't go as far as to force a shuffle, though.