Breeding them would be completely fine! Line breeding can be a good thing, and they're not that closely related. In my case, I love Mr.Gunsmoke and he's June's great grandsire, and I'd have no problem breeding her to a Gunsmoke or double Gunsmoke bred stud. As long as you don't breed to the horses own sire or grandsire, you should be fine (although some people will breed a horse to its grandsire and it can be done successfully). If you wanna see a whole bunch of really closely line bred horses, you can look up pretty much any blue roan Hancock bred quarter horse and take a look at its pedigree lol.
What about Desperados tail? Is it too low or is it correct?
Even if his tail is high enough, or if you bred her to an appy or QH or paint, you could still get a foal with a low set tail since that's how hers is, you're never guaranteed to breed something out of a horse. And you don't want to try to breed to a horse who's tail is set too high to try and compensate, because then the babies tail will either be too high or too low, and probably not correct. Just find a good stud who has a correctly set tail and hope for the best.
But I don't think that's too bad of a fault, especially if it's her only one! And to a non Arabian person, I can't really see what you mean when I look at her lol