There's a lot to unpack in this question, but long story short USAFA doesn't do a branch night like Navy or WP do. My experience is slightly dated, but I don't think things have changed much. Fall of C1C year you will have the choice to list 3 rated (pilot, WSO, ABM, etc) jobs and if I remember correctly, 5 non-rated jobs (weather, intel, logistics, etc). You can forgo the rated options if you are not interested in that. From there, your inputs go into an enigma of a computer algorithm that spit out what job you will get based off class rank. Firsties are typically notified of their AFSC in the Feb/March time frame. A few months after that, they will send out a similar list, but this time it will have options for bases depending on what the outcome of your AFSC. Your inputs go into the same computer algorithm and around 100's night (100 days until graduation) you get your base assignment.
If you want to be a fighter pilot you have to have to 1) get selected for UPT/ENJJPT, 2) finish IFS, 3) finish T-6s 4), track T-38s, 5) hope the needs of the Air Force allow for everyone who tracked T-38s to get a fighter, 6) graduate IFF, 7) graduate B-Course 8) Finally you're a fighter pilot.
For special operations, your best bet is to join the Sandhurst or Combat Shooting teams at USAFA. Its their feeder program for the Battlefield Airmen program. By the time you're a junior/senior, you should get a chance to go to selections. If you're selected, then you can get that AFSC at the same time that all of your classmates get whatever they wanted. After you graduate, you have to go through several more schools/training until you can get your beret and go to an operational unit.
If you want a more in depth analysis of the UPT track,
@raimius has a pretty good thread on it.