Questadt wasn't a Senator--he was chief counsel to the committee. Yes, he was sitting behind Roth in Havana, but that was an editing mistake on FFC's part. In an earlier version of the script, Michael was to confer with Questadt in Havana. That part of the script was ultimately dropped. But FFC had already filmed the Havana sequence in the Dominican Republic, and he wasn't going to go back and reshoot it. So he left in the quick shot of Questadt and hoped no one would notice. He hadn't counted on the sharp-eyed people here!

Put another way: If Michael knew Questadt "belonged to Roth" because he spotted him sitting behind Roth in Havana, he'd never have perjured himself when Questadt showed up as chief counsel to the Senate committee grilling him.

I believe Roth didn’t arrange the Senate hearing: Questadt did:

Senate committees schedule high-profile, televised hearings (like the one on organized crime) months in advance, so the Senators can get the publicity and viewership they need to be re-elected. Roth would have learned about the hearings far ahead, and would have feared that he could be called as a witness. He also would have heard from his political contacts that Questadt was “for sale.” So, he bribed Questadt (as Fredo told Michael, “The Senate lawyer, Questadt, he belongs to Roth”) to keep him informed and to protect him. What’s more, as the chief counsel to a Senate committee investigating organized crime, Questadt would have lots of contacts with law enforcement, including the FBI and the NYPD—very useful to Roth.

When the cops broke up Frankie’s garroting, as Tom told Michael, “Frankie was half-dead, talking out loud about how you betrayed him.” The NYPD would have instantly recognized that they had a potential high-level Mob turncoat, and would have kept his survival secret—to protect him from assassination and to keep possible targets of Frankie’s revelations from learning that they were in danger of being exposed. Questadt would have heard about Frankie’s survival almost immediately.

Bingo! A lightbulb went off in Questadt’s head: He’d convince the committee chairman to ask NYPD to give Frankie to the Feds, where he’d be safer (on an Air Force base) than in a NYC jail or hotel room—and where he could be put to far greater use in the upcoming organized crime hearings. Why would NYPD agree to hand him over? Because they wouldn’t be able to nail Michael for the Great Massacre of 1955 and other crimes on Frankie’s testimony alone. They’d need corroborating witnesses for each of Frankie’s revelations--and they wouldn’t get any. But no corroborating witnesses are required to obtain Federal perjury convictions—only the testimony of one witness and some other evidence or testimony—and the Feds could trap Michael on perjury charges if Frankie’s survival were kept secret.

Then, another lightbulb went off in Questadt’s head: Roth would surely be interested—and would pay handsomely for—the knowledge that Pentangeli was alive and ready to testify against Michael. Roth by that time had escaped from Cuba and had recovered sufficiently from his stroke to listen. Roth prompted Questadt with facts about Michael’s crimes. Questadt was able to turn that info into questions for Michael when he was sworn in. Result: five counts of perjury against Michael.

Roth consistently showed himself to be preternaturally clever in laying traps for Michael, and in recovering from reverses. But Michael had a trump card: his Sicilian cunning. That’s why Michael ultimately prevailed.