The "let's not use cars" debate is quite frankly boring, because in some areas the referee has no choice, and is completely irrelevant to the question posed in the OP.
I think this was handled ok, you spotted that the CAR had flagged incorrectly, and verbally indicated that the play was not offside and that play was to continue.
The goal keeper may not have heard you, sometimes I find it can help to shout to someone, for example, if the keeper has the ball in his hands a shout of, "He's not offside keeper, keep playing" might have gotten his attention better.
After the goal was scored, it was the keepers fault, he should have played to the whistle and not just assumed that play had been stopped, if there is a reason to rule the goal out that can help, for example, if you're at a place where there is more than one game going on, if you're lucky there may have been a whistle that you could have said caused a distraction etc, but I wouldn't go trying to make up a reason to rule the goal out.
In terms of instructions to CARs I always brief mine in the center circle, just before I speak to the captians, I find having the captain's there to hear what you brief the CARs can help later on, as they will know you've told them not flag for foul throws, or to wait if they aren't sure whether a player is offside.