1. The overwhelming majority (aside from like 2 squadrons of 53s) fly some variant of the -60. The MH-60S does a whole bunch of rando missions ranging from vertical replenishment at sea to SAR to SEAL support (only a couple squadrons), and anti-surface warfare. The SH-60R does mostly anti-submarine stuff. Either way, much time will be spent on boats, whether carriers, amphibs, or detachments to smaller ships.
2. Though I'm biased towards Marine aviators, most Navy pilots are just good dudes. I don't really know how to explain it. There's definitely some people who are cocky or arrogant, but almost universally people help each other out (both instructors and students) and will bend over backwards for you if need it. It's a competitive environment because most students (and pilots) are competitive, type-A people, but it's not in a backstabbing or selfish way.
3. It depends. Sometimes it's CIVLANT. Right now, redes options for (Navy) attrites are not great. They're trying to cut people and attrites can make that an easy decision for big Navy. Depending on what community needs people, attrites go on to Surface Warfare, Intel, Information Warfare, Supply, or Aviation Maintainence. On occaision (like if someone has good knowledge and is clearly working hard but completely lacks stick skills, or just barely fails the program) attrites are allowed to become NFOs.
4. After flight school, winged aviators alternate between sea and shore tours. On sea tours, you're assigned to a fleet squadron, are given a division/"ground job," and usually deploy. Shore tours can vary between being in a "production" role (at any level of flight school), or being an NROTC/USNA instructor, staff tours, or some other weird options. Aside from a few very specific ones, almost all shore tours open to aviators regardless of platform, including stuff like TPS.
A large proportion (majority? Not sure) of Naval Aviators are helo guys. Though traditionally most aviation admiral positions go to tailhook it seems like that's starting to change and helo pilots are getting in on the action. In short, you're not really limited in the Navy if you choose rotary or multiengine versus tailhook.
Cross-commissioning is a real long shot. My boyfriend cross-commissioned Marine Corps from USMA and it's definitely not easy (but at least from USMA seemed to have not a lot of logic attached the decision to who could or couldn't? It's weird). If you can, try and get a (Navy) aviation cruise. I dont know how USAFA does training or how feasible it would be, but it would both expose you to the Navy and Naval Aviators and give you some ammunition for cross-commissioning.
Best of luck. Check out airwarriors.com for tons more information about Navy air, training, and platforms.