IIRC the investigation into the true identity of Darth Sidious had led the Jedi to Coruscant through fairly strong evidence (Nute Gunrays walker chair memory cache?), which pointed to one of Palpatines inner circle (at the time not even the Jedi suspected Palpatine himself).
Part of the purpose of the Seperatist attack on Coruscant and kidnapping of the Chancellor was to divert attention away from this line of investigation.
Correct. This is in
Labyrinth of Evil.
Presenting this evidence to the Senate along with Anakins confession that Palpatine attempted to turn him to the Dark Side, combined with the footage of the battle between the Jedi masters & the Sith Lord in the Chancellors office might be enough to stay twitchy trigger fingers long enough.
Possibly not. You forget that the ROTS novelisation makes it clear that Palpatine ensured that the only recordings of the fight were auditory, and he made sure that anything beyond the deaths of Saesee Tiin and Agen Kolar was not recorded. In Court, he or his supporters could argue that they'd been despatched by their fellow Jedi while defending him.
Anakin as a witness is more problematic, for both sides. His loyalty is suspect. To explain:
1. The Jedi Council may not trust him because of his instability and his link with Palpatine, but he is the only person who can confirm the existence of Palpatine's Dark Side abilities for them. However, Mace Windu, if he's true to his word, should trust him if Anakin let him kill Palpatine.
2. Palpatine's camp could clearly influence him along the lines of 'testify against us, and we won't tell you how to save Padme'. It coud be a bluff, but then so was Palpatine's offer.
As far as the public and the Senate are concerned, Anakin is a hero, not a budding sociopath. Remember, he's The Hero With No Fear, one-half of Kenobi & Skywalker, the guy who crash-landed half a starship and rescued Palpatine from Grievous. If he then turns aound and says yes, Palpatine was a traitor and a Sith Lord, chances are people might believe him. Of course, some will say he is simply a Jedi pawn.
On the legality of the Sith:
"The Jedi are the defenders of the Republic," the lieutenant went on earnestly. "Their ways can seem strange to ordinary citizens, but they're on our side. All they want is peace."
"Reallly?" Des said, glancing at his cards and pushing in his chips. "I thought they wanted to wipe out the Sith."
"The Sith are an illegal organisation," the lieutenant explained. She folded her cards after a moment of careful deliberation. "The Senate passed a bill outlawing them nearly three thousand years ago, shortly after Revan and Malak brought destruction to the entire galaxy."
"I always heard Revan saved the Republic," he said.
The commander jumped back into the conversation. "Revan's story is complicated," he said. "But the fact remains, the Sith and their teachings were banned by the Senate. Their very existence is a violation of Republic law - and with good reason. The Jedi understand the threat the Sith represent. That's why they've joined the fleet. For the good of the galaxy, the Sith must be wiped out once and for all."
(emphasis added)
-Darth Bane: Path of Destruction
This is pretty clear, but then there is the matter of what Palpatine said about 'religious freedom' in the ROTS novelisation. If the Jedi could prove that Palpatine was a Sith Lord and the statutes outlawing
the Sith and their teachings remain in force, then they have enough of a case to have the Senate take a closer look at his other dealings. However, if the statues are no longer in force for whatever reason, then the Jedi have a big problem. In fact there is ample evidence to suggest that Vader's identity as a SITH LORD was well known (the Marvel comics series and
The Truce at Bakura are two examples) and that this does not seem to have been a legal problem. Perhaps Palaptine 'made it legal?'
However, please note that in the canon movie ROTS, Windu's accusation of Palpatine being a Sith Lord is neither refuted nor defended by Palpatine - he simply accuses the Jedi of treason after an exchange regarding his power over the Senate, draws his lightsabre, and attacks. The legality of their arrest attempt is not otherwise challenged with regard to 'religious freedom'.
"An elegant weapon, for a more civilised age".
- Obi-Wan Kenobi