Courts are selective about what evidence can be entered. You can't just show up with say reams of papers or random (deepfake) videos and present them.

If you weren't aware of this consider it an awakening. One of the best ways to beat somebody in court is not to have a stronger argument but to prevent them from presenting evidence.

No, in the same way lawyers and the judge can decide ahead of time not to admit an unqualified expert witness, or to dismiss the jury for someone like Darrell Brooks representing himself by bringing up irrelevant information and hearsay which is inadmissible in court. If someone says the wrong thing in front of the jury it is somewhat difficult to erase it from their brains or to convene a new jury.

No. It's up to the judge to decide what to allow as evidence or not. It has nothing to do with your right to a trial by jury.

It certainly seems so to me, but IANAL nor a legal scholar.

I'm curious whether or not this kind of thing was what the Constitution's authors had on mind.

(I've also heard that the meaning of "peers" has changed, but no idea if that's really true.)