Coach,welcome to the board.I'm assuming that you're referring to NFHS(high school)rules,so I'll use them.
In the situation where you received the two fouls,the penalties for the fouls are always administered in the order that the fouls occured.In this case,that means 1 and 1 for the personal foul,followed by 2 shots for the T(all free throws with the lane cleared),followed by the other team getting a throw-in at center.
On the free throw,the clock is supposed to start when the missed shot is touched by,or touches,a player on the floor.It does sound like you had a slow timer,but none of us can really comment for sure unless we actually see it.
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