Think bran maybe used as roughage to unblock anal glads, not an issue ever had with my various greyhounds over the years.
Some racing kennels do walk the dogs for exercise but these are often based rurally so can be bit like a new puppy socialising in a busier urban environment, how they cope depends on the dogs character some find it all adventure others little more wary and need time/space to adjust. Not sure how much work dogs trust do with socialising but worth bearing in mind often racers have only mixed with other greyhounds & not know that dogs come in other shapes/sizes, they do adjust all mine have been dog friendly but do need to be cautious early on & why greyhound rescues send a muzzle home with new adopted dogs (can get some great lightweight full mesh ones).
I use a horse body brush and a cheapo version of the Kong zoom groom which is great for getting loose hair out, don't need much grooming apart from shed twice yearly. I never bath mine unless necessary although all have been no bother.
You may need to brush teeth depending if will chew, dry food doesn't really help as most fling it down the hatch but their narrow mouth shape & genetics has effect on teeth. You may also need to clip nails, but is advise online FB/YouTube on best way to introduce.
I've had a pair of dogs that any poultry based kibble caused soft poo & toxic farts so I now stick to fish based, currently autarky salmon & rice (similar to skinners)and all of my 5 dogs have had no issues with these. It depends on the dog. I always add some water to the dry food, if you leave it to soak it will go soft which some prefer as tends to be what they do in racing to keep hydration levels up.
When you bring your new hound home if they tremble, pant & drool a lot its quite normal & are just bit stressed at change , the sensitive routine loving souls. They may refuse to eat but they won't starve if miss a few meals. New dogs may not want to toilet away from home at first as its leaving a mark of their presence in the neighborhood but will once settled.
About 2-4 weeks in you may find your hound getting a little naughtier than before as settled, confidence grown & testing out what the house rules are. Greyhounds aren't awake long enough to cause some real mayhem like some other breeds 