Personally, I wouldn't ask directly about the reason for rehoming. The relinquishing owner will have gone through this with the rescue, and if there is anything the foster home need to know, they should have been told that by the foster co-ordinator. Reasons for rehoming can often be very sensitive and upsetting to discuss, especially if there are children in the relinquishing family who might be very attached to their pet. You might well find it comes up naturally in conversation, which is great.
I agree about Milgi coats (though of course I might be biased) and yes, Meggie Moo make the most wonderful collars and leads. As far as I know, she is also the only collar manufacturer who regularly safety tests her collars and hardware, something which is vital if you have a greyhound suddenly reaching Warp Factor 12 when they see a squirrel.
Don't forget to ask for their vet vaccination records and their microchip paperwork, and make sure you get insurance sorted. It's handy to have a few spare collar tags made up in advance - I get ours done in our local Timpson.
Have a think about your car, and how/where your dog will travel and if you need to get anything for the car e.g. guards, safety belts, soft comfy beds to lie on (Vetbed is great)
I'd also stock up with a couple of Yankee Candles or similar - greys are notorious for having evil wind, and a move can often cause a slight upset in the tummy.
I hope it goes well for you - once you've got a beautiful pointy nosed creature lying elegantly on your sofa, they become strangely addictive and you find that one is never enough. We currently have four (three greys and a lurcher). Finally, you should also be getting plenty of support and assistance from the rescue organisation - there should be a named contact you can talk to regularly to ask questions and discuss how your new arrival is settling in. If there isn't this, then go to another rescue. Sadly, there's no shortage of greyhounds needing homes and there are masses of greyhound/sighthound rescue organisations around, which vary considerably in their standards. Some are brilliant whereas there are others I wouldn't trust with a stick insect.