Hi Wendy,
My wife volunteers up here with a cat rescue group an dwe have more than our share of foster cats in the house, waiting for adoption, and have more than my share of cat knowledge, so if you have any questions, feel free to ask!
Litter tracking problems, we have a combination of those plastic "litter catching" things you get at a pet store, and a piece of carpet sample (free from Sears, I believe; just ask).
Counter problems. We use, what I call the "Spray Bottle of Discipline." None of them like getting sprayed, though once in a while, they jump up, just to checke things out (usually when we're not around, or asleep).
Bathing. We have a "dry bath" powder if one of them smells weird, for some reason. For big messes (sprayed with mud, etc.) you can turn on your shower, close the curtain, throw the cat in one end and close the curtain so force them to run through the water out the other side of the curtain. That forces them to lick and clean themselves thoroughly, top to bottom. Haven't had to use this method more than twice.
Spaying and shots. Definitely check around for the various animal/cat neutering programs that are around. The one up here in CT (if I remember correctly) spays/neuters for $50 (as opposed to $200+ at a vet), with a couple of more bucks for shots and flea meds.
Claws. I agree that declawing isn't good. It's basically amputating the first digit off all their toes. And you definitely don't want to see how a cat looks at a vet's office after the surgery. You can get "soft tip" applicators for cat claws, but they wear out after a while, and They're probably a pain in the butt to apply. An easier way is to cut the claws with a finger nail or dog nail cutter. You may have to get Lima Bean used to it slowly at first, by just playing with her(?) toes for a while; then moving on to playing; then "introducing" the cutter (as in sniffing, getting used to it near her toes, etc.); then cutting only one claw . This can all happen one right after another, or it could take weeks. But it's worth it.
Good luck!
Seriously, on your photo what cave system are you in? I did the Cheesepress in England years ago which was like an 15 inch squeeze to get through. Entrance to that was up a freezing cold stream, and a February to boot!! Am finally going to marry caving ("spelbunking" you say over here?)and diving this November when I do a course in Crystal River, FL, allegedly. 
