1] Ninja use ritual gestures (mudra), especially hand gestures, to manipulate aether. Usually, a mage tips the balance of their own body's aether (or aether in their immediate environment) towards a specific element (lightning, fire, etc.) and manifests that raw power. Ninjas draw aether from a variety of sources and conjure unique, specific "frequencies" of it. So far, we know of three; Heaven (energies in the air), Earth (energies in the land), and Man (energies in the body). By conjuring and combining these aetherial energies, many new effects take shape - depending on which energies are used in which order and balance. Even though it's not though of by ninjas as literally magic, it's clearly similar.
2] There are perhaps more mudra, and almost certainly at least more shapes the energies can take. However, the in-game mudra (Jin, Chi, Ten) encompass a triad of forces that are often seen together in the real world. They're the Three Realms, the Three Powers, etc. If I was going to fudge the system for the sake of roleplay, I'd probably stick with "unknown combinations" rather than "unknown mudra". Seems a rather large liberty to take without precedent.
3] Ninjutsu was developed on an island called Hingashi (meaning east, meant to be similar to Japan). Due to its smaller, isolated nature, the area was constantly in strife as its people battled for control. Because of this, the shinobi that developed ninjutsu were not a single group. Just like real-world martial arts, every clan had their own unique styles and teachings. Based on what teachings your ninja learns, its bladework and magicks might be different.
2 & 3] If you were going to roleplay things that weren't in the game, this would probably be where you place the blame. You know mudra or ways to combine them that the Doman shinobi currently in Eorzea do not. Perhaps you acquired the teachings of another clan somehow. But you'd have to ask other ninja roleplayers - I don't RP, myself, lol.
4] Possibilities are limited only by your imagination! (And the canon, I guess, depending on how much your roleplay troupe respects the canon. It seems to very from group to group by ... quite a lot.)