I can understand not being entirely happy with having a pet you didn't choose to have... I still consider myself a dog person, even though I don't have a dog anymore and I have two cats, lol.
One of mine is great, the other I find a bit bemusing, she's sweet when she wants to be, but I'm fairly sure she's only in it for the food :D I'd never do anything to be cruel to her, but it's to me not like having a real pet, in that, she'll only play when she wants to, or be affectionate when she wants to and she'll randomly decide to be all bitey or disappear for the day - I know that's what cats are like, but I do sometimes wonder what the appeal is.
I wouldn't complain about her though, because I chose to get her, knowing full well what cats are like - but yeah, I can understand being a bit peeved if you've taken one in rather than chosen one.
Covered litter trays are so much better, they can't miss and they can't kick litter everywhere, I know they advertise themselves on you not knowing they've used them, but you do, you can still clear them straight away - it just stops the mess spreading.
Cats are a bit sicky, but if it's more than once or twice a week, I'd be taking her to the vets, even if it is just furballs, you can get stuff to clear them.
Dry food makes one of mine sick (she's ill, it didn't used to) because she eats it, then drinks and it swells up so she's sick, I'd try leaving food down all the time and see if that makes a difference, in case she's over eating because there's a limited supply if you see what I mean.