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we took our son at 5 1/2 months. we didn't take him in the pool, our choice, so i really can't answer that.
we did take him in the infant carrier into the restaurants with us, we didn't take in the stroller, just the carrier.
You can bring your child in the pools with a swim diaper on!
And you can also bring your car seat in restaurants (I'm assuming you're talking about the infant carrier kind of car seat). I think most restaurants have a special stand that holds the infant carriers. I've seen them myself in some restaurants but I don't know if they all have them!
He can go in the pool with the disposable swim diapers on, I'd recommend getting them BEFORE you go to Disney, they're very expensive there.
I've never had a problem taking a infant carrier car seat in...alot of sit down places won't let you take a stroller in, but counter service places I just wheel the baby right in and let him eat from his stroller.