One website that will answer all your questions: GreyTalk.com
But I'll try to sum it up for you
Karen was right. Greys can not be let off leash unless in a fenced area. This will most likely be written into your contract so if you do, it's going to be a breach of contract. The whole on/off-leash topic is highly debated, but it'd be safest to err on the side of caution.
As you've noticed, Greys are quite unique from other dogs. Thus, it'd be preferred to find a vet that has prior experience in Greys and similar sighthounds. This will require a bit of research on your part because some vets don't understand the intricacies of Greys. For example, Greys have terribly thin skin. What may start as a small, superficial nick on Grey can turn into an open gash that would require stitches. Because of a Greyhound's thin skin and coat, they will need a coat if you live in a colder area. My rule of thumb is, if I'm cold, my Greyhound probably is, too. When it hits 40-45 degrees F, I'll put a light coat on Giselle. You can easily find coat and collar merchants here:
clicky
Don't worry about the flea med sensitivity. As long as you use reputable brands like Advantage and Frontline, your dog should not exhibit any intolerance. Actually, I don't even use these meds on Giselle. Her coat is so thin and easy to groom that I have never seen a tick or flea on her.
Karen also mentioned how Greys are usually not exposed to "home life". Up until the dog has entered foster care, s/he has most likely never been exposed to stairs, linoleum floors, glass doors, etc. However, if you find a good adoption group, they will have exposed the Greyhound to all of these and more. They will also have cat-tested the Grey to see if it is compatible with cats. Otherwise, many Greys have a rather high prey drive and WILL chase and kill the household cat, even if the two have been co-existing peacefully for years. Just a few months ago, one of the adopters from my group had her cat killed by her Grey.
I can't think of much else that hasn't been mentioned, but if you'd like me to go into more detail, please don't hesitate to ask!

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