Does age matter when it comes to getting the K1 Visa approved ?

No. That you are both 20 is not going to affect his ability to get a fiance visa. However, proving the legitimacy of your relationship is the major obstacle, and one that is heavily scrutinized by the consulate in the Dominican. Before you file anything, do yourself a favor and consult with a lawyer. If the petition is not done properly the first time, and it gets denied, appeal is almost impossible and subsequent petitions are much less likely to succeed.

Not necessarily but being young may mean not enough documents at hand. You may want to speak with an attorney as it could save you time and money should the case be denied. Many attorneys like myself will speak to clients over the telephone if they can not come to the office.

No. The fact that your both of the same age does not affect him at all. At the time he has the appoinment at the Embassy in Santo Domingo he needs to bring evidence of the bonafide of the relationship and that is going to be the key for the approval of the visa.