tl;dr I don't think they're dumb enough to actually hang him, hanging him is like throwing away the lives and impending return of some of their own men in UA captivity while throwing away your chances of getting concessions in negotiations and ensuring that an investigation will conclude with a missing prisoner or a well-reported war crime. Givi and a lot of the Motorolovtsi say a lot of dumb shit when they're "emotional" (screaming in ppl's faces) but the people who tell them what to do aren't crazy.

IMHO, Doubtful. Once someone is filmed on a video they publish, it's essentially a given that he's also released either in a pre-negotiated mass-exchange of prisoners or in an individual exchange that's captured on video and published on all the pro-rebel channels.

Second, wasting a ranking officer is a terrible idea. Like ISIS-level terrible. Your officers get captured, too and you need to get them back in exchanges. That or an officer is worth a lot of soldiers or even some concessions at a negotiation like Minsk. If you're fighting a war against a larger force as the rebels are, and you kill an important enemy officer who has ties to political groups involved in the new government and military, you can basically expect them to crap straight down your throat, no mercy.

From the outset of the conflict when Strelkov interviewed the SBU officers he had captured while they were trying to capture Bezzler and retake the Gorlovka SBU building, he pretty much devotes a portion of it to saying exactly which sorts of officials he holds in addition to those SBU guys and their ranks and not only shows that the rebels understand the value of an officer but also that they will release hostile officers in exchanges that account for their rank.

Then, there's the fact that it's going to be investigated since he's an important person and that rope-marks on the neck after shaming parades are signs of war crimes and not of combat injury.