Are you permitted to bring your own...

Are you permitted to bring your own cooler/drinks to the pool?

yes

You cannot bring alcoholic beverages to the south pool because there is a bar there. They say there is a law that forbids one bringing their own alcohol. I suspect that goes for the ocean front deck also. I believe this is true although I learned this several years ago. I suspect the policy has not changed.

Yes you can, except for the south pool and sun deck, due to state liquor laws governing Loggerhead's.