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.

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

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.