Go early. Great suggestion about alternating with the gardens. I think they're better fun. More to explore. Plus, safer, fresh air.
Yes the house is open for tours. It is self guided so if the house is crowded you could visit the gardens first, then go into the house. I would recommend seeing both while you're there.
I believe it so, I was there last Saturday and the house was ipen to visits, however, you need to wait in line so not all the people get in there at the same time.
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