If my renewal for registration is due..and falls on a weekend of my date. Will dmv give me a grace period and not charge the $14.

Yes they will

Do it ahead or find a AAA that's open on Saturday .

Just go to AAA on the Friday before and pay it. And there is no question.

Yes

Your registration doesn't have to be paid on the exact date that it is due. You can pay it early to avoid any confusion .

I do not think so since you can renew 24/7 on line.