Burger - the throw-in has to be taken in the first place for it to be retaken by the opposing team.
First caution for delaying restart fine, restart is as originally awarded - second caution for delaying that restart, restart is as originally awarded.
Awarding the throw-in to the other team would generally come from a foot or hand 'foul' when delivering the throw-in or, despite being told where to take it from, the throw-in being taken from the wrong place. You often see the former but less so the latter as the referee can boss the position of the restart (throw-in) by using any or a combina