When Mace Windu told Anakin, "If that's true, you have my trust," that was the statement that doomed Windu. Skywalker should have been trusted by his Jedi friends in the first place. Qui-Gon Jinn was a quasi-rogue Jedi who didn't follow the code and he was trusted for the most part until he offered to train a young Anakin. Skywalker's trust was placed in Darth Sidious long before Windu finally agreed to trust him. By that time, it was too late for Windu and the Galactic Republic.
In the fight between Mace Windu and Darth Sidious, Mace Windu was winning the battle. However, when Skywalker interfered he gave Darth Sidious time recover. This cause Darth Sidious to ultimately beat Mace Windu. Without the interference, Mace Windu would have won. I do not believe that Darth Sidius was faking.
Mace Windu has forgotten more about being a Jedi Master than you or I combined could ever possibly know. Although Annikan Skywalker decided to intervene to hog all of the glory, his intervention was completely unnecessary. As his later life as Darth Vader proved, Skywalker was not a team player. But he was not necessary for Jedi master Mace Windu to wreck shop.
If Darth Sidious actually lost this fight, then many things have to be asked. Why did he tell Anakin he was a Sith Lord? Why did he let Anakin leave his office after Anakin told him he would report him to the Council. He was expecting the Jedi Masters to come. He also knew Anakin would come and "rescue" him, and the movie shows Palpatine talking to him through the force at the moment the duel starts that if he dies, all hope of saving Padme will be lost. He just did this to seduce Anakin. He would have toasted Windu otherwise.