Can you visit the grounds at any time, or is that only on the 3rd sunday as well?

Only on the 3rd Sunday. Sometimes they do it more often check the website. It is well worth the visit and take a ride on the little train.

The 3rd Sunday of every month, June, July and August 1st and 3rd Sunday. 11 am to 3 pm!

Only third Sunday.

Generally it's every 3rd Sunday, but they also have a few random free public days that they open.