Yes you can bring anything and everything but not pets.
Yes you can. I recommend it as purchasing there can be expensive. Also consider bringing water shoes if planning on going in the rocks or sliding down the length of the falls trail. It is not sharp bit slippery so the extra grip from the shoes can help stabilize you. Very good idea for kids. Buy them somewhere other than the falls. They were expensive when I was there last and if you are bringing a family it all adds up.
Yes
Yes to both.
Yes, just no pets
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