The answers to your questions are fairly personal. Some people insist on running tires down to nothing, and/or do so for financial reasons. Other people throw-out or give-away tires that present them with any doubt whatsoever -- correctly calculating that any resulting injury costs more than a set of tires.

That said, one of those seems to be starting to delaminate on the sidewall, as my last Gatorskins did, and many of them do. I did not continue riding on those tires, but many people do.

I'd keep running those other tires, from what I can see, but that opinion is worth almost as much as you paid for it. It's your call.