“Or can one simply come and say ‘so and so’ molested me, do a writeup of how that abuse occured, and file a suit asking for monetary damages?”
Yes, you can file a lawsuit for just about anything. You may not win, and the judge might throw it out before you see a courtroom, but as long as you fill out the paperwork correctly and pay any necessary fees, you can file it.
“My question is - before these accusations are made public, is their a standard of proof that is required that goes beyond simply writing a statement on what was done?”
No, unless there is some kind of gag order by the court, the standard 1st Amendment freedoms apply. You can go accuse anybody of anything publicly, but if you do it maliciously, you open yourself up to be sued by them.
That remedy doesn’t help much for celebrities, because they are held to a different standard in a libel or defamation suit. They are expected to endure a certain amount of negative speech about them simply because they are a public figure. So, for example, I can say “Obama is a two bit street hustling conman”, and have little fear that he would be able to win a libel suit against me for that. If I said it about my neighbor, he could probably get a payday.
Also, celebrities generally have plenty of money, while those accusing them may not, so suing false accusers for libel, even if they win, is more of a symbolic victory.
the fact there are putures and multiple stories of defacto orgies (without women present) speaks volumes.