I think you're confused because many companies choose not to comment on pending lawsuits. That doesn't mean they are legally forbidden from doing so. Tesla has every right to defend itself in the court of public opinion, though certainly if this goes to trial, the parties will seek jurors who haven't preformed an opinion based on public statements. IANAL.
It's perfectly fine to prejudice court proceedings that are not yet in progress (though less so for prosecutors attempting to do the same in criminal cases).
It's not permissible to influence the deliberations of jurors, but that's a narrow scope--jurors aren't supposed to digest media related to the case while serving, so the parties can generally say or opine whatever they want during a case outside of the courtroom.
The ideal resolution for Tesla is for the guy to drop the suit. This is what they're trying to accomplish by laying their cards on the table. IANAL either, but I'm not sure what risk you're talking about - do you suspect this suit will go to a jury trial, and it will become difficult to find jurors that haven't read this press release?
But the lemon law lawyer posted a video of himself walking around in a courthouse with a duct-taped paralegal following him around. That's what "going to court" is, right?
I'm not sure what you're implying. Is the car manufacturer not allowed to give their side of the story publicly when a lemon law claim is filed against them?
I don't know the answer to your question but I suspect Tesla is more concerned with the truth getting out and telling their side of the story than just the outcome of the case. Although to be fair, that is merely a guess and a personal opinion.