I don’t believe in allowing a cat roam around outside. They kill birds and other wildlife and they poop in flower beds and gardens. They can really be a nuisance, especially if they are doing these things in the neighbors’ yards. I know some people allow their cats outside and that is their business. I just personally wouldn’t do it. An outdoor cat has a considerably shorter life expectancy because so many things could happen to them outside (dogs, wild animals, cars, getting caught in something, etc).
Do cats kill and eat squirrels? If the cat has a high prey drive and the squirrel is within striking distance (i.e. not clear up a tree), then yes they can.
Is it safe for them? Squirrels tend to not have diseases like rabies. They can have parasites though, which a vaccine would not protect against.
Would that cat know to come back inside at night? Well, cats have minds of their own. They may or may not want to come back in. If they are hungry and they are fed inside, then they will come in. If they are eating squirrels and it’s nice outside, they may not. Depends, I suppose.
Are cats okay to live with rabbits? There are people here on BB with cats that live around bunnies with no problems. If a cat had a high prey drive though, how are they to know that those bunnies are not something to attack? My childhood cat snatched a gerbil from a cage in my bedroom that I was “baby-sitting”. Luckily I say him trotting down the hallway with his prize and was able to get him to drop it.
To be honest, I think there are probably better solutions than getting a cat to kill the squirrels. You could get a live trap to catch them. Or you could enclose the tomato plants with rabbit fencing (like a cage over them) to keep the squirrels out.