Can one do an Acting performance while invisible? (Trying to see if I could get the bonus to Virtuosic Performer to apply while invisible)
It depends on what you are trying to achieve. Why are you rolling Performance?
to Inspire Courage/Inspire Heroics
If you strictly follow RAW, it isn't said in Inspire Heroics or Lingering Composition that you need to use the same type of Performance than the following composition. So, per strict application of RAW, you can use Acting and then Sing.
But I'm pretty sure most DMs will find that ruling a bit weird.
Then, for acting, it states that it's Drama, pantomime and puppetry. All have a need for people to see you. So, if you use an acting Inspire Courage, it should not affect anyone who can't see invisible.
this puts a big dent in my Invisibility plans if I cant inspire courage ugh. Would I however be able to perform a Lingering inspire courage and then go invisible and have it work for the next 3 rounds?
Well, on paper, it looks like the answer is yes. I don't find anything stating that you need to see the Bard performing during the three rounds.