Palpatine being the ultimate Sith lord, and really the persona of evil, it would seem that ANY opposition must be controlled. Either wipe it out, or put in fake opposition to keep the public in check. Were the Jedi-friendly/Republic-loyal senators killed off?
No, but some certainly were
Many senators loyal to the Republic served both before and after Palpatine took power. Among them were Bail Organa (who was indeed one of the leaders of the Alliance) and Mon Mothma (same). Of course, their survival depended on hiding their true feelings from the Empire.
Bail Organa felt like he was being buried in bureaucracy. His office in the royal palace on Alderaan was roomy, and he’d never felt overwhelmed in it before. There was more than enough space for chairs, a desk, and the aquarium full of brightly colored sea creatures he’d had installed to keep his daughter from getting under his feet, but he felt like all the room in the galaxy wouldn’t accommodate the double weight of responsibility he now carried. He did what he could to represent the people of the Alderaan sector in the Imperial Senate, and he did what he could to help the people of the galaxy when he was sure no one was watching.
As to why Palpatine couldn’t simply execute all the pro-Republic senators right off the bat when he first took power, the answer is that they almost all were pro-Republic (initially). Sure, many of them cheered the creation of the Empire, but if you had asked the senators a month after the creation of the Empire, whether they had loved the Republic, they probably would have agreed. Don’t forget, they’d just fought a long a vicious war (well, sent others to fight it for them, on the whole) to maintain the Republic. They saw the Empire as the natural successor state to the Republic. Some of the senators most loyal to Palpatine probably were those who had been most loyal to the Republic previously. What distinguished Bail and Mon Mothma is that they were loyal to the ideals of the Republic, but it would have been hard for Palpatine to determine that from, say, their speeches: all the senators, as politicians, likely paid at least lip service to the Republic’s ideals.
In addition, some apparent dissidents, such as Gall Trayvis, were secretly Imperial spies, so Palpatine did carry out the questioner’s idea of creating fake opposition to lure in his opponents. Presumably, if the Empire was too efficient in killing Senators with Rebel sympathies, people would be more suspicious of people like Trayvis, and Palpatine may have left some alive for this reason.
That said, Palpatine most certainly did execute senators whom he believed to have Rebel sympathies. One prominent example is Nadea Tural, who was imprisoned, along with many other senators, at Arrth-Eno:
It’s not clear whether all the people here are senators, but if they are then Palpatine imprisoned at least thirteen of them:
He later executed them and pinned the blame on the Rebel Alliance.
Within the Legends continuity (apparently established in one of the RPG supplements), it would seem that at least some of them were killed off:
Warrants were issued for the arrest of all suspected Rebels. Stormtroopers burst into the Senate, and hundreds were detained. Some—those learned to have had Rebel affiliations—were never seen again.
There is no evidence that he did the same in the current canon and, as DaaaahWhoosh pointed out, Mon Mothma certainly survived, as did Bail Organa, the man who raised Leia, at least until Alderaan was destroyed.