To speak on the drills to strengthen your short game, I could go on for days because I consider the short game to be from 115 yards and in. But to narrow it down I will start with pitching and work our way to the green.
Pitching is all about distance control. When you can control how far your ball is flying and rolling or stopping then you can attack pins. An easy drill for distance control for pitching would to simply pitch the ball about 50-75 yds out. On the next 5 balls, pitch the ball so that it lands and stops before the previous ball. On the next 5, your going to start out with the first ball pitched to 25 yds and then pitch the next few balls between 5-7 yards further than the previous. This drill will help you dial in those numbers when you are close to greens.
Chipping is a much simpler drill. All I have students do is set their wrist first before taking the club back. After that is borderline a lag putting stroke depending on the length of the chip. Forward press, set the wrists and then use a lag putting stroke. Simple. Once they hole a chip, they will never forget the move.