1. Your height would not disqualify you. If you are in shape, you should be fine. Become as fit as possible! Other officers can find a reason to give you a hard time if they want to! If you are a good recruit, and then officer, it would likely be mostly in jest. Some criminals will use what they can to intimidate you, and capitalize on what they perceive as a weakness. Don't let them!
2. K-9 and mounted can be very competitive!
3. Having a GED as opposed to a high school diploma would not make a difference (especially if you have a college degree from an accredited school).
Good luck! Keep us posted, and let us know if you have any other questions.