No problems with livestock what so ever mine live along side my free range hens even when left alone all day with them they will not harm them. I could introduce anything to them even pet rabbits once they know they are off limit they will not touch them. Think of the livestock they co-exist with in their native lands.
Well doganjo, Borzoi simply translates to Sighthound, so if you were Russian you may well call them Borzoi as they are Sighthounds just without the western refinements .
These dogs pre-date the creation of the Russian breed we call Borzoi considerably and do not originate from Russia but from Central Asia.
Rosemary pop up and see us we are just by Brechin, we have the Dog Grooming Shop 'Tidy Tails' in Brechin.
Saluki and Tazi, Taigan, etc are just regional variants of a landrace of dogs stretching the length of the silk road. Only in the western world do put them into separate breed boxes. In their native lands one type simply merges seamlessly in another as the environment moulds them to suit.
They could be could good fun for racing but I would doubt they would take it seriously once they have seen live game.
As for health testing, a millennia of natural selection to be able to survive the harsh conditions of the Middle East and Central Asia has forged possibly the toughest and healthiest dogs imaginable. Don't confuse these dogs with western show dogs.
I went to Kazakhstan in 2007 to attend an aboriginal dog conference.
http://www.flickr.com/photos/7270140@N08/sets/72157602119982718/Nura the mother was bred in the US by a friend, she has the most wonderful loving and steady temperament you could imagine.
Best Regards
Mark