There is a link to information on camping if you search for the website for the seashore. We are not campers, but did drive by the Bird Island site where the waters are calm and some people do kite surfing there - interesting to watch. Some people also were fishing there. The water is shallow for quite a ways so to fish need to wade out. Hope this helps.

The USS Lexington is located at Corpus Christi Bay across from the Aquarium. It is not on Padre Island. I recommend both and making a day of it.

No, there are other back ways to it.

Yes, we walked our two dogs on the seawall next to the beach. There were dogs on the beach itself as well.

The Rangers would be the best ones to answer this question on the day you are there. It really does depend on the tides and the amount of rain expected.

Large nice parking lot - definitely accessible. Probably so about the restrooms - great set up in the visitor's center but I didn't notice any others while we were there. Hope you have a great time - a fabulous place to enjoy our Texas coast

We where there in December the weather was very pleasant we golfed I did not go in the water but there were families playing the water

I don't know about renting a jeep but you can rent 2,4,6 seater golf carts and I think I saw a place that also rented ATV's but not 100% sure on that

you will be fine, just be careful, and not stupid. I found driving on the sand fine.