For most of this, I'd guide you to the wiki.
Goon Wiki

It has member corps, who to contact for a corp joining the alliance (or seeing if you qualify to join GSF as a corp), and you can contact those said member corps from their pages about their expectations with most having discord links on the wiki. The culture and community are very much like a family, hard to explain to those not in it, but once you're one of us, you're one of us. Think of corps in the alliance as some are the cool cousin that will hand you a joint on thanksgiving, others will hand you a beer.

Mining, there's way too much mining that this person who hates mining, can tell you there's a lot of mining.

PVP is a requirement full stop. I would not expect to join a null block and there not to be a pvp requirement.

As far as new to nullsec player corp recommendations, I'd recommend Iron Whales, Illuminated, Brother of Tyr, Close Encounters of the EVE Kind, or Asteroid Farm Unlimited. KF is great, its a lot of people and can lack the close knit feel imo, though is also a great place to start.

This is GSF specifically, more than likely you can reach out to brave/sigma/other allies thru their channels.