No. Unlapping is not done to get all the drivers onto the same lap again, but to get slow cars that are in the Queue in front of faster cars out of the way. And seeing as Perez was pretty much at the back of the field they would not let any lapped car overtake as it is not required by the rules. It's only done when it is safe to do so and if it makes sense because having slower cars in the mix during a restart could be dangerous.

No, it’s about the order. The idea is not to mix drivers that are a lap (or multiple laps) down with drivers competing in the same lap.

I think Perez would have been to pass everyone once so he becomes the last driver and that is it. (Assuming he was not last to begin with)

It’s about the order of the drivers not so much about getting everyone in the same lap.

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.