Yeah, you have to sweetspot the knee.
To counteract the fact that the knee had so much raw power, they made the hitbox for the very small ( in order to make it harder to hit your opponent with). Basically, to get the full-powered hit from the knee, you have to time the hit within the split second that the knee is at full power.
Also, when you play as Falcon, you need to be the aggressor in the match. Although Falcon has to be offensive during a match, that does not mean to play him stupidly. For instance, sometimes you need to run straight at your opponent, sometimes you need to mindgame your way to them. As with all characters, variety is essential. With some of Falcon's physics and his horrible recovery, if you don't play aggressively, you will be heavily punished and probably lose the match very easily because you can't make a transition from defense to offense.
Falcon basically has two methods of attacking his opponent : first, a shffl'd aerial. Here, you have five options, all of which can be very useful. To answer your question about n-air, yes you should be using it. The reason it is important is because it is the longest-lasting of Falcon's aerials. While all the others are very quick attacks, the n-air lasts slightly longer. So if another person expects a f-air and plans to shield-grab out of it, the longer animation from the n-air would hit him. Again, as with all characters, using a variety of moves is essential.
The second method of attacking your opponent is very simple : jump-cancelled grabs. Grabs are important in Falcon's game because they very easily lead to aerial combos, usually with a full-powered knee. Also, if your opponent is expecting you to use shffl'd aerials and is shield-grabbing in anticipation, you can use Falcon's pure speed to just run up and grab-combo him.
If you need any more tips or character specific-advice, PM me.
edit : One more thing about the n-air. Falcon has wonderful horizontal jumping when you short hop and fast fall, and the n-airs extended attack animation and range is really useful from closing in on your opponent from a distance ( think FD ).