Oh boy, a character I actually played in the MMO and can kinda talk about. In DFO, Inquisitor has two main mechanics and it kinda looks like they are carrying over to this game.
First, she has two different debuff effects that she can inflict on enemies. One coats them in napalm and the other causes them to burn over time. If an enemy is ever affected by both napalm and burn, they explode. The explosion is different depending on if you go napalm -> burn or burn -> napalm.
Second, she can light her axe on fire. When her axe is on fire, her attacks have better range, do more damage, and burn enemies automatically. The ability that ignites her axe is an uppercut-style attack called "Holy Fire" and she can cancel other specials into Holy Fire to start it up mid-combo. It kinda looks like the Inquisitor in the trailer cancels an attack into Holy Fire at 0:11, but it's not clear since there is a jump cut right after. None of the footage so far in any trailer shows her axe just passively burning, so I am not sure this mechanic is being added, but it would be kinda weird to drop that since it's her most iconic feature.
There is a really pronounced white flash effect that you can see in the Duel trailers every time a character performs a special move. In the MMO, that same effect is used to indicate a special cancel, but in this game it seems to appear any time a character performs a special, even if they aren't canceling it. There's also a red flash effect that a couple moves have, and I am 99% sure that this effect is indicating a move is invincible (or maybe just armored). Fstriker's DP (Rising Fist) has the red flash, as well as Berserker's eruption move (Burst Fury) and one of Inquisitor's attacks (Noble Rage).