In a first down situation in example; 2nd and 3,it's the
Fourth qtr. 12.00 mins. to play team gets a first dwn.
My question is "Does the clock stop to move the chains and if so when whole game,last 2 mins. etc."

Under High School rules (those 48 states that use NFHS rules), the clock stops the move the chains for the entire game. If this is the only reason the clock was stopped, the clock then starts on the ready-for-play.

Same goes for NCAA.

Yes, but let's be explicit
 

Yes, in Federation rules the clock stops on ALL first downs. It starts with the ready for play as long as nothing additional occurred to cause the clock to stop and requiring it to start at the snap (i.e. out of bounds)or there IS NOT a CHANGE OF POSSESSION. Let's not forget the clock starts at the snap on a first down following a change of possession....