A rule of thumb I was told years ago was to look at the audience if you are talking or singing.  When you are playing, look where you want the audience to look, since they will tend to follow that cue.

So if you're doing something tricky that you worked on and want them to notice, yes, look at your hands.  If you don't, they may not notice it as much or may think it wasn't something all that impressive anyway.

If someone else is doing a solo or vocals, don't stare at them, but keep glancing, like you are paying close attention.  Act like you are enjoying it as much as any audience member, and you've just got a much better spot to watch from.  It gives a better impression of you as well, like someone in a conversation who knows how to be a good listener instead of just someone waiting for their turn to say something.

If something goes wrong for another player, don't stare and look puzzled.  Say the drummer is having an issue with their hardware or a bass or guitar player's amp is doing something unexpected or maybe somebody broke a string?  Get your eyes on some part of the performance that is going right, instead.  That can help smooth things over instead of calling attention to the problem.

Cameras, I don't know so much about.  But as someone who watches videos, I can say I think it can be anything from a bit "wooden" to kinda eery if a player is staring into the camera steadily while playing. 

Facial expression I don't think I've ever been good at.  I tend to be kind of "dead-pan" when playing.  But a thing I have seen that can quickly detract from a performance is if a person is using facial expressions that just don't fit the music.  You see it sometimes with singer, especially the ones that got told at some point that they'll "project" better if they smile.  So they're singing about people dying and losing lovers and terrible tragedies with a silly smile pasted on their face.  That always seems like either a very odd mixed message or downright creepy.  At the very least, you know they aren't paying attention or being at all moved by the story they're singing or that maybe they just don't care.  Not the best message to the audience.

If it is an audience that can applaud or react in any way and they react when you come to the end of a song, at least look up and nod a small bow.  Performance is a communication.  You play and that's one part.. They applaud or compliment and that's another.  If you just do nothing, they may feel like it was either a deliberate snub or that you don't like applause or compliments.  That's a quick way to get less audience reaction, even if they really do like your playing.