He didn't regain his composure. He gave himself completely to the Force and imo entered a state of Oneness.
When your defenses are being overwhelmed and you're proclaimed to be THE master of the most defensive form things are not going well. He had to give himself completely to the Force to land a counter on Grievous that allowed him to gain the advantage in their fight.
Actually its outright stated that Grievous was more inconvenienced by their environment then Mace was and he still stalemated him actually going on the defensive after taking a few moments to completely analyze Mace's form.
You mean considering that Cin Drallig is featless aside from bing roflstomped by Anakin? Lol. Kit Fisto who is stated to be one of the the best swordsman in the history of the Jedi Order is stated to be Shaak Ti and Obi Wan's ( in Cestus Deception ) direct superior and has a form and fighting style that is well suited to fighting Grievous's own along with the fact that Grievous was injured at the time.
I don't doubt that Vader could defeat any of the Council Members aside from Mace or Yoda if it's an all out fight but we're talking about pure lightsaber skills. Formidable sure but so are the Council Members. I would considering Vader has had his guard pierced by no names on several occasions and was having trouble with Old Ben.