Is it accessible for wheelchairs?

Yes, there are a few areas that you can't get to via wheelchair (due to historical preservation reasons) but you can access the majority.

From the front, no because there are stairs but they might have a side entrance. I would call and see.

Dirty as usual

Yes (with qualifiers) You won't be able to go into the fern room, which is the original 1910s installation and has steps, a stream in the path, etc The other rooms are paved, wide enough, and mostly flat. The floors may be slick however-- I slipped multiple times. Would highly recommend a chair over cane or crutches for that. Depending on your tread, how used you are to your chair, etc, that might be fine or might be a hazard. There are "bonus content" paths you won't be able to take-- they're narrow, unpaved, up a lip, or all three-- but you can see everything from the main path as well. It's there to get you closer to it. I liked them bc they let me avoid people, but they weren't inherently more interesting. You may have to do a U turn and backtrack on one paved path, bc the other end is stairs, but there's space for it and it's a pretty outlook. Extensive grounds outside worth looking at. Dirt is dirt, but there's gravel sections as well, and the pond is amazing

Yes