If you choose for the creature to gain haste, it gains haste indefinitely. It won't lose it as the turn ends or as another player gains control of it.

You divide the damage as you activate Skarrgan Hellkite's ability, not as it resolves. Each target must be assigned at least 1 damage. In other words, as you activate the ability, you choose whether to have Skarrgan Hellkite deal 2 damage to a single target, or deal 1 damage to each of two targets.

If a creature entering the battlefield has riot but can't have a +1/+1 counter put onto it, it gains haste.

Riot is a replacement effect. Players can't respond to your choice of +1/+1 counter or haste, and they can't take actions while the creature is on the battlefield without one or the other.

Once Skarrgan Hellkite's ability has been activated, it resolves even if all +1/+1 counters are removed from it or if Skarrgan Hellkite leaves the battlefield.

If Skarrgan Hellkite's ability has two targets and one becomes illegal, the remaining target is dealt 1 damage, not 2.