Yes
I'd advise being careful on the main ramp into the cave- it's wet and there's some gravel. Might be a smart idea to have two people push a wheelchair in.
Yes, you can go into all the park areas. Only a small portion of the cave exhibit is inaccessible (5-10 min worth at fat man's squeeze in main hall). I'd say it would still be a very good experience.
Not the whole cave. There are areas that are.
Thanks! Your answer is awaiting moderation.