He probably would have had to stop for new tires during the unlapping... The rules made as a result of the Hamilton / Verstappen debacle in '21 don't allow much room for variability in unlapping now..
No. The safety car doesn't even have to wait for the unalapped cars to catch up to the pack. We saw that in Bahrain. There were still a couple of seconds between the cars that unlapped themselves and the pack.
Racecontrol may extend that period if they deem it necessary. They might have let Perez go one more lap around to ensure he is at the end of the pack during the restart. But I don't think anything in the rules would force them to let him catch up in laps.