First of all, high-five for wanting to foster dogs! That is an AWESOME goal and I am so glad somebody wants to do it!
I don't know about certification, but I doubt it. They will probably just come check out your house, the height of your fence, etc. Nothing huge.
About greyhounds: You should know that in spite of their reputation for being huge runners, they are actually huge couch potatoes! They can go FAST when they want to, but they only need a really good run once or twice a week and they are calm, content dogs the rest of the time. Greyhounds rescued from tracks are generally very shy and nervous. I would work on not allowing biting or snapping, even out of fear, and tons of acclimation to new things, like cars, roads, new people, cats, fountains, busy parks, other (nice) dogs, etc. I do know that greyhounds like company and it's great if you can rescue two or three together - they will entertain each other, help each other feel at home, and calm each other down when they're nervous. It's best if you do a multiple foster to get dogs that have known each other for a long time - for example, were in next-door kennels at the track, came from the same litter, etc.
Here's something else that just came to me. If you are planning on fostering more than one dog, it is best to start with just one, get that one used to your house and yard and basic-obedience trained before you get another one. Two nervous, frightened, not-at-home dogs that don't know each other are a recipe for disaster. As I said you can get two littermates or kennelmates together usually without a problem.
The bully breeds. As you said, by nature sweet dogs. I agree with that completely. However, fighting dogs are trained to do just that - fight - and whether American Pit Bull Terrier or Golden Retriever, fighting dogs are mean. I would be very, very aware of the dog in question's backstory. Were they rescued directly from a fighting ring? How long did they live under such conditions? Do they have behavioral problems like barking, biting, snapping, growling, possession guarding, etc. that you should know about? I would recommend staying away from any dogs who are just plain mean, but a shy or frightened pit bull can be rehabilitated and that is the kind of dog I think you should look for to foster. Be aware if they are not good with other dogs as greyhounds are not good at protecting themselves.
If you're going to keep multiple dogs, it's also a good idea to get the greyhounds first. A mixed dog of the pit bull background may become very possessive of your home if they are no other dogs there to begin with. My dog came to us when we already had a dog of three years, so she knew it wasn't her house. A pit bull entering a house already "owned" by other dogs will be more submissive, both to them and to you, than if you get the pit bull first.
You should know about something called pack discipline. Pack discipline is a frightening thing if you haven't seen it before and don't know what it is. A bit of wolf history: wolves live in packs. The alpha male is boss and if alpha says to do something and another dog doesn't do it, the alpha will usually go for him, roll him on his back and growl a bit to teach him a lesson. This is what may happen in your home with multiple dogs, especially at first.
When we got my dog, Cali, our other dog, Sandy, didn't know what to think. He's a very laid-back dog, but instinct kicked in big time. Cali is a big barker, so every time she barked and wouldn't shut up, Sandy would come right on over and nip her, maybe snarl a bit, and then back away and look at us fearfully because he knew he shouldn't bite. But he had to - again, pack instinct. We let it go on without correcting him for it, and in a few months, he stopped doing it and hasn't done it since. Cali learned her lesson!
So if you see your first dog, the dog you rescued first, nipping or snarling at another dog, it's usually pack discipline. Don't interfere or problems could develop. It's very quick and you may miss it if you aren't looking for it. If your dogs get into an all-out fight, teeth and claws flying, up on each other, growling and biting, that is NOT pack discipline. Use something - not your hands! - like water, a stick, something, to get them apart and then separate them for a time-out. Real fighting should be a capital crime in multi-dog household.
Teach them to be good on leads together so you can do group walks, which are very fun and will draw interesting looks from other people. Play a lot. Play games that exercise, like tug, fetch, and hide-and-seek, and play games that teach thinking skills, like hiding a treat under one of three cups and mixing them up, and then telling them to find it.
Best of luck to you! Have fun!