I don't know of any way to stop a cat from hunting, it's what cats are made to do. It's instinct to bring the prey back to the den, so my best advice is to monitor her when she comes in and make sure there's no prey in her mouth. I usually try to accept my cat's mice good-naturedly, make "yummy" sounds, and give her a treat to distract her while I dispose of Mr. (or Ms.) Mouse properly (she is an indoor cat, but we live in heavy woods, so every fall is "mouse season"). Also, if she is an outdoor cat and a good hunter, make sure that you keep up to date on any vaccinations and parasite (worm/flea) control that your vet recommends. You can't prevent her from hunting or bringing home the catch, but you can keep an eye on her to make sure that she's not bringing her prey in the house.
Counters? Don't leave food on 'em. Cats like to get on counters because they're high. You can try keeping a barricade of empty tin cans around the edge of the counter, but that usually doesn't work for long. You can also buy a plastic carpet runner or chair mat (with the little hard plastic nubs) and put it on the counter with the nubs up...but again, they figure these things out. Best bet is to keep unattended food off the counter.
A cat tree can sometimes help by giving the cat a high place of its own, but as long as there's food left on the counter, it's fair game for the cat, and you can't really fault her for jumping up there.