Fireteam options evolved a lot in late N3 and N4. There are so many wildcard troopers that I could easily have a full core fireteam just composed of wildcard troopers. Is that allowed? Assuming it is not, and I have a fireteam with 4 wildcards and 1 original trooper, can I reform the team after the original trooper is killed?
Only if at least one of the Wildcard troopers can also form their own Fireteams (Like a Veteran Kazak, which can form Haris, Duo, and Core) No
You can't form a fireteam using ghosts, imaginary troopers, or dead troopers unless you're playing the unreleased halloween sectorials. Seriously, the rules don't have any notion of "reforming" a fireteam. If you disband a fireteam (or it gets disbanded due to coherency violations), and you want to form a fireteam again with the same troopers, you don't get any special permission just because the models were in a previous fireteam. You have to satisfy all of the fireteam creation rules again with the troops you have now.