In my experience, assuming you have enough thickness/volume of agar media, you are looking at 2-3 weeks. Although, honestly, I've tried longer but this is the most conservative answer I can give you. If you are in doubt of the potency of the antibiotic, use a control plate spread or streaked with E. coli simultaneously with your experiment. Of course, the best approach is you should make new agar media but maybe you are having some "I-don't-want-to-make" agar media moments, which all of us do. Good luck!
That depends a lot on humidity in the storage and how sterile was the hood where they were made, but generally unless they dried out (less than 50% of original agar thickness) or got visible fungus, they are fine even for few months if you need to just simply replate something. I wouldn't use anything older than 2 months or so for cloning though.
I totally agree with Oleksandr, the humidity in the storage e.g. within sterile plastic bags and the sterile practice are very important, anyway, in my experience is better to prepare them only a few days before the experiment less then 2 weeks.
I had using LB+carbenicillin+X gal wrapped in plastic wrapper and aluminium foil stored probably up to or more than 1 month in fridge and its still works well. I think as long as the media is well protected from light and not dry out then its good to use. But please take notes that i am not using amplicillin which is less stable than its substitute, carbenicillin antibiotic.
LB plates with XGal can last a long time, until they have dried out. However ampicillin has a much shorter half life when in plates stored at 4 ℃, probably 2-4 weeks and you will already have significantly decreased the effective ampicillin concentration. This leads to satellite colony formation if you are doing transformation / cloning experiments.