What you or the video player is doing is not in itself illegal. The "illegal" part, if you want to use that terminology, is the purchasing and/or possession of an illegal copy of copyrighted material. The fact of copyright infringement doesn't magically emerge through the process of playing it.
There are not—as far as I'm aware—any laws against watching copyright infringing materials; intentional possession is the entirety of crime.
No. Copyright is about making a copy. It’s literally in the name: right to copy. A file downloaded illegally means someone made a copy without being authorized by the IP holder.
There are 'performance rights' that are separate from the direct copyright infringement. i.e. if you buy a DVD legally and show it to your church's youth group, you'll be infringing on the performance rights. AFAIAA there isn't an 'enhanced' punishment if you got the IP illegally, just two separate offenses.