You can usually fly between 60-100 hours per month, depending on whether you're checked out in both of the main fleet types or just one of the fleets, on time of year, on the group you're assigned to if flying military work. Some military groups will only do a couple loads all day, while some other groups will turn non-stop from sun up to sun down. Just depends on what they need and how much of your tax dollars they show up in hand with for converting Jet A into noise.

There is a fine line between being too pushy and not being heard from enough. As others said, making an in-person delivery of your resume at least gets your face seen and you can give your 'elevator pitch'. If you're a good talker and catch the CP at a lull in the chaos you may get the chance to ride along or talk at length. Otherwise, I don't know, maybe follow up every 2 weeks or so? Just a guess.

As for the culture, well, it's a drop zone. Everyone is there because they like skydiving. Make friends with skydivers, maybe do a tandem at the zone and mention your interest in being a pilot, etc.