Well, the PSA scale is explained really well here:
https://www.psacard.com/resources/gr...andards/#cards
As to ?AUTHCTY, that's their term for "FAKE" and it is likely done to stay on the side of not getting sued if they happen to deem it fake and it is later found to be real.
To your other ones, I'd have to see them. But the one with the 4 likely has a light surface crease visible on both sides. Only seen on the front can get a 5, only seen on the back can get a 6.
But yes, you can review the card for a higher grade. If it "bumps", they reslab it with a higher grade. If it doesn't, they mark the damaged areas with a sticky note and arrows. Costs the same as a regular submission. Sometimes I'll use my 15 freebies for renewing my subscription to review cards where a bumped grade increases the value well enough. Maybe there is enough interest that the next time the board does a bulk submission, we could also submit PSA graded cards for review as well.