Question: How did Matrix know that the gun store had a hidden room full of illegal weapons such as automatic rifles, rocket launchers, and anti-personnel mines? There isn't any dialogue explaining how he knew the room was there and how he knew the general location of the hidden switch to open the room.
Answer: You are right that there is no reason given in the movie so any answer would be speculation. One possibility is it is a secret government (or criminal) arms cache which can be accessed in times of emergency and Matrix is connected enough to know about it.
He might have heard about it through the grapevine as gun guys talk. Notice how he fumbles around for the switch? That and the surprised look on his face when he walks into the secret room says he had never been in there before but had enough knowledge to know there was one.
Question: Why were members of John's former team given new identities?
Answer: Possibly so any surviving enemies they encountered on previous missions and or tours of duty couldn't hunt them down and kill them for revenge.
Question: The villain's whole plan was to force John Matrix to kill some foreign president by holding his daughter hostage. So why at the beginning were they killing members of his unit? That seemed rather pointless to me.
Answer: They didn't know where Matrix lived. They were killing Matrix's old unit because they knew if they did General Kirby would make physical contact with Matrix to warn him. They simply followed Kirby to Matrix's home.
Answer: To flush him out into the open. By killing his unit it will make it more likely he will want revenge and come out into the open making him a target.
Chosen answer: A sexual implication, suggesting that it's something Bennett would find exciting.
Tailkinker