I am not a lawyer, and I'm an US-centric, so I'm answering only for the US.
Original poster = the one who posts the material in question.
End user = the person viewing the video.
How does one know FOR SURE a piano performance is or is not copyrighted?
There is no way for an end user to really know, unless good copyright information is provided by the original poster.
Even if an end user asks the original poster, they may be confused about copyright issues or even outright malicious.
An example would be a musician who infringed on a popular song, but still he claimed on the video to have all rights secured.
Too, they say that a link is not copying, per se, but merely a means of directing people's attention to what may or may not be copyrighted.
A link is not copying, but knowingly linking to infringing material is illegal.
Innocently linking to infringing material is legally gray, but it's likely legal.
Is YouTube liable when an individual posts a link to a copyrighted performance shown on their site or is the individual liable?
The original poster is responsible for copyright. This is in the ToS and is also part of the safe harbor of the DMCA.
Believe I read that YouTube is often contacted by companies or individuals who ask them to remove their copyrighted materials, performances, etc.
This is correct. This is a part of the DMCA.
Youtube is not a content provider, but only provides a platform to distribute content. If a copyright owner sees something infringing, they can file a DMCA notice with youtube and take down the offending material.
The original poster can also file a DMCA notice to put back the offending material, although they take a large legal responsibility in doing so. They testify that the material is legal and in doing so, they cannot claim they they didn't know it was illegal.
I believe this is one of the new computer related legal issues that has not been thoroughly addressed by the courts thus leading to confusion.
Well, three cases have proved that knowingly linking to infringing material is illegal.
Plaintiff Intellectual Reserve (IR) vs Utah Lighthouse Ministry (ULM)
Universal City Studios, Inc. v. Reimerdes
Comcast vs. Hightech Electronics Inc
As far as I know, there has been no cases of innocently linking to illegal material.