I want to say first that I do not like the idea of potion effects on or having to do with enchantments for tools - enchantments are supposed to be upgrades of the weapons that have to do with enhancing the tool's current qualities, not adding new ones; Sharpness, Efficiency, Unbreaking, Fortune, Power...these all increase or upgrade things about the weapon itself, whether the durability, damage, speed, or block breaking (Fire Aspect and Flame are exceptions, but then again fire is not a status/potion effect). That being said, it is just my opinion, and your suggestions are actually pretty good and decently thought out.
A nice idea, but really this sounds more like a potion affect akin to Saturation more than an upgrade to your pick/shovel. I do see the advantage it would give in mining would be nice and not too OP, but since 1.11, hunger has been highly buffed, as AntVenom showed in a video a few months ago. So really it only saves about two seconds of eating every 5 minutes of mining or digging. Not OP, but not super useful, kind of like Smite or something.
So basically Auto-Smelt from Tinker's Construct? I always like this idea, but what's the point of furnaces? None of the other enchants completely replace certain functions in the game, so I feel this one is just a bit extravagant. Even in TC, you still don't get the double reward that you get from a smeltery, but as you said, it can be combined with Fortune. More thought into this than most, but also a bit OP, making gapples as common as oak trees.
This actually isn't a bad idea, but it also depends on a few variables: maybe it is exclusive to Mending and how much does it increase XP level? I feel like maybe a 20% increase in XP but being exclusive to Mending would work out pretty well.
Again, it depends. I think this is decent, but maybe only +1 damage, or half a heart, per level? Not super effective against diamond armor, but want to keep it balanced
Here we go with the potion effects, I will try to keep my bias against the out of the way. Not bad, but maybe for less than two seconds? Also, I see your previous conversation, and it looks like you said it would be most useful in fleeing from better-geared opponents. True, but...Slowness dramatically decreases FOV, especially at level 5, meaning it would be simple to jump around your opponent, and they won't be able to hit you with their tunnel vision, meaning they might as well be AFK. This is a good concept, but may need tweaking so that it doesn't mean your opponents can't even hit you.
There isn't much to say about this one, it just seems natural and isn't too OP. IT would have to be a small decrease though, imagine a diamond axe with Sharpness 5 with half the cooldown of normal! Maybe each level adds 5 or 10%, so it won't be noticeable, but still a decent advantage.
Hmm, it seems you forget the whole super-regen with full food bar from 1.10 or 1.11, I forget which. This would be nice before then, but after, it seems redundant. Maybe if you were fighting a team and didn't need to spare time for food, but they would never be able to kill you with that kind of health regen. As it is, you have to eat food to get it, making it relatively realistic. So, nice idea, but both OP and redundant.
Why not use a splash potion? It might be a bit inconvenient to get a brewing stand and gunpowder in a UHC match or something, but in SMP, it would be fairly easy and much better. I feel this one is similar to Endurance, we have better alternatives, so what's the point.
And the reasoning behind this is what exactly? Again, interesting idea, but let's face it, nobody is ever going to sneak during matches where this would be useful. Sacrifice mobility to reduce damage...but what about shields?
Not a bad idea, actually. It would be a distinct advantage against bow users, for sure. I don't see many problems with this, at the moment.
But...we have Ender Pearls. It would be a bit faster of a getaway, instead of having to wait for the pearl to hit the ground, but what if your enemy teleports in front of you with lava? This might be good for escaping from better-equipped players, but...kinda depends on how well they are geared. They can still shoot you.
Old idea, and gapples give you absorption for that, and are actually not as rare as you might think. It would be better, as those hearts would actually regenerate (I'm assuming), but having level 2 on all armor would give you almost double health, and level 3 would more than double. It would take hard grinding to get, yes, but that's the trap many games fall into, have a hard grind to get something OP so you can keep other players from getting it. In my opinion, just OP the way you described it. I would be more comfortable with one level at +1 heart per level.
Drawback and Range:
You did credit those ideas, which is nice, and they both seem to have similar situations to Recharge. Drawback maybe has a top of -20% time, and Range maybe has +20% range (too much and the arrow might fly out of render distance :P). Good as long as they are not too strong.
This almost seems too OP. It would be nice if you were on a mountain and they would have a tough time reaching you or returning fire, but at close range it would still be a distinct advantage. If the duration was too short, the nausea would not distort the screen long enough to actually do anything, and if it was too long, it would give your opponent no chance of hitting you. This could be good at a very distinct timing, but I don't know how best to keep it balanced.
Finally, you admitted that this is slightly OP, but is only really so at level 2, which is tough to get. I just feel like this isn't that bad, but it depends how it's made; if it was like Aimbot (which I HATE), then no, but if, as you said, it went to the closest entity in sights, with a certain limit depending on the level, then...I actually don't have much of a problem with that.
There you have it. I spent an hour typing this, so make sure to read it thoroughly