Question 2 - No, you are confusing the PUP list with IR list. IR list there is no such thing as a waiting period. Once injury settlement is reached he cannot be re-signed by the team again. Although, I think they could still be signed to the PS, a loop hole the last CBA didnt close up. I could be wrong on that one though.
I looked this one up and talked to an agent, and this one is incorrect. A player can resign by the team he settled with after six games, plus the regular season games he was paid for or settled. So if a player was only paid for two games in the settlement, he could come back by week 8, roster or practice squad.