Replying to Questions for Jackson locals

I want to go to Jackson and ski Corbet's and S&S.

Regarding Corbet's: How long does it usually take patrol to get it open after fresh snow? A few hours? A day or more?

Regarding S&S: I've heard various rumors. "It's always closed." "You need ski patrol permission to ski it." "You need to sign a waiver to ski it." I don't know what is and isn't true. Are any of those claims true? Is it ever open, or does it always require special permission (assuming you don't want to duck a rope and get your pass pulled, obviously)? If it does require permission and/or waiver, will patrol let you ski S&S any time Corbet's is open?

Asking because if I make the drive to Jackson I want to make it count and ski the lines I want to ski, so I would like to choose dates accordingly to ensure I can ski them.

Thanks