Does the park provide carts/wagons for carrying camp stuff in to the walk-in sites?

Think it does. I recall carts parked near the trailhead heading down to the walki-in sites.

Yes it does

I didnt see anything like that while we were there

Yes, up by the bathroom near the Outdoor Adventures bike stand, there are carts.

Yep, top of the trail by the bathrooms and bike racks

Depends on which side of the park you're on. For instance, where I was on the water entrance did not.