Ambush reaction to counterspell

How does the ambush keyword works when played like a reaction spell? A permanent normally doesnt create a chain for the opponent to play a card so is it the same thing when you play ambush creature cards?

For example, my opponent plays a spell (he has focus) and i react by playing rengar on the battlefield.
Can i play another reaction card again after playing rengar? Is the focus back again to the opponent right after playing the creature? Can the opponent target the rengar while he enters the battlefield or only after he enters?

Thank you for your response!