Hi Ginger! Welcome to the world of ferals, LOL!
First of all, when you trap feral or stray cats, they should not have any interaction at all with your pets - or be in an area where your pets go. Not before they see the Vet. It's not so much FIV or FELV which are fairly rare unless a colony is infected - it's that you just never know, and it is not worth the chance of infection or disease. Or parasites.
I don't know how it works with your vet, but ours is very sympathetic to the cause of strays and ferals, and we were able to take them directly to the Vet as we trapped them. A cat was in the trap - boom, we slipped a blanket over the trap, put it in the car, and off to the vet. What they would do is board the animal in a cage until they could see it. We had them tested, then vaccinated and spayed or neutered. The Vet would call us when we could come pick them up. For males, it was generally the same day, evening or the next day. For females, depending upon the weather, it was usually several days before we picked them up. They did use disolvable stitches when spaying (You might have to ask your vet to do that - if they're not used to working with ferals, they might not think of it themselves) so that we did not have to retrap the cats and take them back to have stitches removed. But because of the healing involved with the spaying, the females usually stayed at the vet anywhere up to five days. If it was raining and foul weather, we did not release them right back, but let them board there for a few days. But our vet was willing to give us a discount on everything, because we kept them busy with lots of animals. I think the best thing to do is to call your vet and chat with them about it first. You may find you want to contact a local SPCA to see if they have cheaper vet services for ferals. But you'd have to tell them you're starting a trap-neuter-release program (which it sounds like you kind of are!)
OK. Now the other questions...
As to feeding them.... there are a number of ways to handle it. It depends upon how much work you want to put into this.
Let me go get some links for you.
But Gary and I started by just putting out bowls of food at a set time every morning and night. We used paper bowls and threw them away when we were done. We put out about a cup of dry food for each cat. That got expensive. We then built a feeder. It works for when you go away for a few days, and it keeps out almost all animals except raccoons. I don't know of any way to prevent them from feeding on the cat food. There are a lot of raccoons around here, and for the most part they really aren't much of a problem.
If you want to start simple, you can just put out a bowl of food for each cat you're aware of each night. If there's any food left in the morning, you're leaving enough for everyone to eat. You'll probably have more strays and ferals turn up. (That'll probably happen anyway.)
If you want to discourage birds and other animals from eating the cat food, using an upside-down laundry basket with a hole cut out so the cats can get in helps stop birds. (Use the open-laundry baskets - you know, with the lattice-work on the side).
But I will get the link to the feeder. It's not difficult or expensive.
We choose to put out water for the cats. You live in Florida, so access to water probably isn't a problem. Access to clean water would be the issue. We purchased large plastic bottoms for potted plants. They require cleaning daily. Birds like them too. It works for us and it was cheap.
Feral cats shelter anywhere they can. You can construct shelters for them. They may use them, they may not. I have seen a lot of creative ideas on this subject. I don't know what your property is like or what would be appropriate. The main thing is to NOT use blankets or anything inside. Fleas or ticks, etc. get in them, and getting rid of them again would be a nightmare. The main consideration is simply to provide shelter from weather. A large plastic laundry basket/tub type thing (not with the holes, something solid) would be fine for FL. Put it up on those palates that they use for moving boxes on and off trucks - something to get it up off the ground so it's safe from rain. Cut holes in both sides of it. This helps them feel safe - several exits for escape. Stuff a little hay in there. Replace the hay if it gets wet. They'll find that comfortable and safe. That's one idea. You'd have to put several out for four cats. Perhaps one for each, although we found that the ferals often piled in somewhere together - but they were from the same litter of kittens. We don't provide shelter for the adult ferals here - there are so many natural places out of the weather for them here. But I'll get the links for shelter ideas too.
DId I get to all the questions? Let me know!!! ...and I'll go find those links for you.
Don't forget - there are some red "stickies" up at the top of the Feral Colonies forum. They've got trapping ideas and hints, and a lot of resources. Save Samoa does too.
Ginger - I think this is so wonderful of you!!!!