I'd say I'm a casual Halo fan. I've probably only put about 50-100 hours into each Halo's multiplayer (aside from 4, which I only played for like two hours), so I can't claim to be an expert, but I think it's really hard to judge the Spartan abilities in a vacuum.
As a big fan of the way Halo 5's multiplayer feels, I think the Spartan abilities work really well for Halo 5. The maps are designed in ways that take the clamber into account, the thruster makes for some interesting one on one encounters and quick escapes, and I've even gotten some fun kills with stabilize. Even if I'm always annoyed when I get killed with a Spartan charge, in general, I think these abilities gave Halo 5 an interesting, aggressive feel that I've missed since Halo 2.
That said, I know there's a lot riding on Halo 6, and a lot of people want it to be a mechanical return to Halo's glory days, so here's how I'd personally try to balance things.
Sprint, charge, and slide are so interconnected to me that I think you can't have one without the other two. As much as I enjoy sprint and the way it's balanced, I would remove them and increase the overall movement speed. Not to Unreal Tournament levels or anything, but just enough that you feel like you're moving at an impressive clip. Halo 1's movement at 60fps in the MCC feels really smooth and swift, but still has weight to it. I think that's a good place to start, with maybe a slight speed increase.
I feel like the utility of the thruster would REALLY change if sprint was gone, so this is something I'd have to playtest, but I'd keep it in for now. I like how it can mix things up in a one-on one encounter. I think I'd keep the distance of the boost the same. It's just enough to allow you to reach certain clamber points, not far enough to help you avoid an enemy with a shotgun.
I've got no issue with clamber. Halo's jumps have always felt kind of floaty, so I think the extra press of the A button gives vertical movement a little more physicality. It might be a bit less useful without the sprint, but I think it does a good job of leveling the vertical movement playing field.
Ground pound can go. It seems kinda flashy and fussy, and it's made me mess up aerial melees before. It's also an extra function on a button that already has a use. Let's toss it out.
As for stabilize and smart link/ADS in general... I'd drop 'em all. Limit zooms to certain weapons again. Maybe I'd give stabilize to rebalanced forerunner weapons and tune down their tracking capabilities or something, but that's more of a weapon balancing issue than a specific skill one.
Hopefully that'd help strike a balance between old and new-school Halo.
As for your second question...
It's also hard to judge that in a vacuum! I think finding a happy mechanical medium would be a good thing, but I don't mind the idea of giving players more options. You could even make the arena players older, less customizable Spartan IIs and give players crazy, super tweakable Spartan IVs or something. Given that Arena and BTB are Halo staples, and REQs fundamentally make Warzone modular, I think that it could be a good idea. The only problem is giving characters two avatars and having one of the game types not play like Campaign... It's a complicated issue!