Is there still an admission charge and reservations required in November? I can't find it anywhere on the website. It seems to say open from May to October. Can I still get in?

The park is closed . You cannot get in as it has a specific entry gate which is closed now. Please visit below link for additional details https://www.nhstateparks.org/visit/state-parks/flume-gorge

The park itself is closed.

The place is close now till next year

I believe that it is closed for the season