For 1, that can just be another Skill check with the Thieves Tools, or have it be that he has to succeed with the check by more than 5 to accomplish the extra stuff. Something the normal Expertise would be able to accomplish, no need to nerf.
For 2, that’s not how Arcana is supposed to work. Arcana is just what you know about magic. It has nothing to do with manipulating it in any capacity. A Barbarian Zealot can have Arcana as a skill, it just means you know about magic. So you’re already changing the skills into something they’re not. Which, hey, kudos to you, but would the Barbarian be able to do that too if he had expertise?
For 3, I’d just have him make an attack roll (shove) and let him narrate how he kills the guy. If he really wanted to make sure he doesn’t grab the ledge, an Athletics check could be done, but in the end, it’s just narration. I’ve had players saw the head off a dragon, rip a guy in two and throw the pieces at a fleeing enemy, explode the heart of a Tarresque, perform a new Mortal Combat fatality where they smash the guy to the ground and the use their giant hammer like a golf club to hit the guys head, sending through his body and out his butt to sail through the air...I mean the tales are endless. And I don’t require a special roll. They brought the enemy’s HP to zero. They get to narrate what the death looks like.
As for the expended resource, that’s just another resource to keep track of, gumming up the works, and nerfs the Rogue, which is unnecessary. The Rogue already gets only one attack, only light armor, and no spells unless you choose Arcane Trickster, which only gives 1/3 castor status. The Rogue can do two things: Sneak Attack, which isn’t guaranteed, and be better than anyone else at a select number of skills. Why would you take that away? Do you nerf the Paladin’s Lay On Hands feature? At lvl 20 that’s 100 HP of free healing to be divided out as needed, and from a primarily combat class. What about the Champion’s crit on a 19? Or a Sorcerer’s Points? Why do high skill checks have to provide such a problem when every class has things they can do better than anyone else? Why do you need to force your players to trade a class skill to kill someone in an awesome way, or force them to expend and keep track of a resource on what the developers felt should be a permanent class feature? It is needlessly nerfing it. It’s SUPPOSED to break Bounded Accuracy. Every class gets to break something. Fighters get more attacks than anyone else, Barbarians can take more damage and deflect attacks with their pecks, Bards get to do literally everything while seducing all the stuff, Clerics get to destroy Undead, Druids get to shape shift, Monks get an ungodly number of attacks and eventually can karate chop with the strength of a battle axe, Paladin can Smite, Sorcerers can break magic, Warlocks can do a no save 10ft push with every beam of Eldritch blast, Wizards can learn every spell in the game, and I’m sure Rangers can do something cool too, WHY DO YOU HAVE TO PICK ON ROGUES AND ONE OF THE ONLY THINGS THEY DO WELL???
(Yes, I know Bards and the Prodigy Feat get it too, but they get it later than Rogues and Bards literally do all the things.)