You didn't make mistakes, but it might have worked better to do it differently.
A lot of the difficulty of running Fate is in picking a useful mechanical model for current events, as opposed to applying the rules correctly. That said, let me address your mechanical concerns first.
Attacking Multiple Targets
This is enough of a concern it's got its own paragraphs in the core book - look here for "affecting multiple targets". Short version: yes, but you have to split your total attack roll among your targets and they only defend against the part they got. Good for mook sweeping, not so much for harder targets.
Creating an advantage can create an obstacle multiple people have to overcome, and special circumstances or equipment, like a rocket launcher, can legitimately hit multiple stress tracks at full strength. But by default, your attention is divided.
Fate Points Per Scene
Maybe it feels a little off in this particular scenario, where some of you might have been on the NPC's side, but yes, no matter the opposition they're commanding, the GM gets Fate Points equal to the number of players.
A smaller number of targets are usually taking fewer total actions than the players, so having more concentrated Fate Points tips the scale there.
Doing It Differently
So, the problem with a full-on grind-on-your-stress-track conflict is that people can take lasting consequences to stay in it. That would make sense, if the GM wanted a scenario where everyone was so at loggerheads that they might wear themselves out before the enemy army even landed.
It doesn't sound like that was what you were going for, tough, so I think in this case a contest would have been a better model. It doesn't sound like anyone was trying to cow someone into submission, just make the most compelling argument. In the rules text on contests, a debate is even called out as one of the scenarios that suits a contest. (Specifically "a public debate" - yours sounded more private, but it was still more about getting your point across than shouting someone down.)
Set some total number of successes, everybody takes turns trying to win a round by getting the highest available result, creating advantages risks your turn on success, most total wins takes it, allied sides of the argument can combine successes to share the victory. On the surface it fits what you were trying to do pretty well, but only you can make the call.
