Yes, they are at the Village Rentals and Provisions area just inside the entrance. $10 for a single, $14 for a double. All of them have a sun shade and a small storage pocket. However, it is first come first serve (no reservations) so if it's a busy day you may want to bring your own just to be safe.
Yes as you go in they can be rented. They will also allow you to bring your own into the zoo. They are like ten to fifteen bucks if you rent one.
They have cheap ones
Yes they do have strollers and wagons
Yes they do.
Yes
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