I don't think there is any difference between "dating" and "seeing." Being "romantically involved" shows a little more commitment.
Dear, sweetie, honey, hun, and babe are all terms of endearment for someone you are romantically involved with.
Yes, it's very normal to go out with friends of the opposite sex - as friends - when you are dating other people. I'm married, and had dinner with a friend of the opposite sex just this week.
If he is going out with them on "dates" as opposed to just going out as friends, then he doesn't feel you have an "exclusive" relationship - when you are exclusive, you don't date other people. If that upsets you, then you need to talk to him about whether you want to both be exclusive.