Blue Shift is at least considered partly canon, I read somewhere that the teleportation works like Dr. Rosenberg explained it did (not that anyone was listening.) On the other hand, Rosenberg and Co. will almost certainly not return in any sequels to come.
Barney won’t have a big role in Black Mesa because 1: You can kill almost all the security guards in the game and 2: Which one is the real Barney. The mod takes the safe route of assuming that Blue Shift is canon, and have him be the guy pounding on the door at the start of the game.
“About that beer i owed ya” is a reference to “Hey, catch me later; I’ll buy you a beer,” a line spoken by security guards if you try to “use” them pre-cascade. If you are extremely nitpicky, Gordon was probably promised a beer before the beginning of Half-Life, for whatever reason.
“Just like old times, eh Gordon?” did not necessarily mean that he and Gordon fought alongside each other. I believe that he was simply referring to all the legendary ass-kicking Gordon did back in Black Mesa, and the shootouts with Combine soldiers reminds him of those he had with HECU soldiers back in the day, and that he knows Gordon had too.