A note about destructible walls: There's a puzzle at the end of DC that makes the final boss easier. Without spoiling too much, I'll tell you that some of the items you need for that are behind a destructible wall.
So if I just want those special items, how many walls I would need to break?
For the puzzle? You should only have to break one. It's in the same part of Hollow Earth as the industrial bot (this will make sense when you get there), supposing it isn't randomized where they end up. I only beat the game one time so far, so I can't tell you if that's the case. The other required components you'll find in other parts of the DC, but you should come upon them naturally as you dig around down there.
So on that note, loot everything.
And how big is the re-spawning the problem? Especially asking those that finished DC with recent patches that did some re-balancing. If it is too hight, I would probably do heavy stealthing (have around 180 stealth), just to avoid wasting resources. It is not like I can carry all loot and go to shop.
It isn't nearly as bad as it used to be after the latest hotfixes, but it can still be a huge pain if you don't get how it works. While you're in certain parts of the DC, you'll stack up a debuff called 'Creeping Dread', the enemies don't start to mass respawn until that ticks up something like 20 times and changes into the 'Eye of Tchort' status. That's when the Tchortling Boogaloo begins. Up until then you can run around out of stealth and not have too much of an issue, outside of some annoying snail enemies that only spawn in a couple of areas. Oh, and rathounds, not even the DC are free of those.
The Mushroom Forest is a different story. You'll probably want to sneak in there as often as you can because it's full of annoying enemies that deal out tons of bio damage, and the mobs/the entire area both hit you with a debuff that nerfs your max HP. So fighting there in general is a pain.
And then there's the deep worms in the labyrinth...stealth is definitely an advantage in the Deep Caverns. It isn't really worth it to fight anything down there you don't strictly have to, that's my advice for you. They're all annoying bullet sponges.
Regarding enemy resistances, what kind of grenades are most effective? I guess low level frags would suck due to enemy DT?
EMP's are useful in the part of the DC with robots. Frags and HE are pretty useful too, but I'd only bother with MK III's.
How often can repair kits be found in the DC? Are other types of kits important to stock up?
You can find some in the warehouses, and occasionally in other areas. I didn't really watch for them since I ran a full-psi build. If you're worried, definitely bring a ton of your own and just shove them in a locker at the storage depot when not needed. You'll probably be going there a lot. The DC is all about backtracking.
Note that I also have in stock one antitermic galvanic overcoat and good metal armor. Up to this point I barely ever used them. Would it be a waste to carry then to DC? I would think so.
If you have CAU armor I'd just bring that and forget about everything else.