Hi Menkary,
It looks as though our corp, Filthy Peasants, fits your list of requirements for a corp. While we’re not huge we are a decent size and regularly have 10-20 people online during US TZ which is our peak timezone. We’ve also managed to get more than that for big fights. We are a lowsec pirate corp that lives in Solitude and while our primary goal is pvp we also have our hands in various other activities such as industry and drug manufacturing.
If you want to do a variety of things in eve without having the pressure of a null block while also having people around to support you this may just be the place for you. Convo me in game or join our public channel Open Filth.