Gators do not use saltwater as their swimming area. It has to be FRESH water.

No. I've camped there several times and saw no gators on the beach. This doesn't mean there are no gators in the vicinity - it's definitely surrounded by marshy wetlands - but there won't be any to bother you at the beach.You can definitely see gators on your drive into and out of Rutherford if its warm. You can see them (mostly juveniles) sunning themselves along the roads. I counted 25 the last time when we were leaving. It was pretty cool to see so many! If you go during the spring or fall migrations, you can see a lot of birds too.

Be aware of your surroundings, and you should be fine. I kept my dog on leash at all times after seeing a few gators.

We overnighed there twice. Never saw gators but we did see folks venture far down the beach with all manner of campers. Id be more concerned about high tide, soft sand, getting stuck irreversibly. or meeting folks you might not want too. we stayd close to where we entered the beach, on hard sand.

While it's not impossible, it's highly unlikely as you seldom find them in salt water. The only gator we encountered was on the drive out there from Lake Charles, when we had to swerve hard when one truly ran out in front of the truck.

We never saw any and we were there a few weeks ago.

No gator issues/sightings when we camped on the beach in Jan 2019.

No, gators don't hang out on the gulf of Mexico.