To answer your questions in order:
1) You won't get the plot at all unless you're familiar with Nitroplus VNs, many of which weren't translated into english. On its own, the normal story mode is no different than your typical crossover fighting game. There is an extra story mode you unlock after clearing story mode once, which is similar to BlazBlue in that it's part Visual Novel and part fighting game. You play as different characters for each chapter, which can help you learn them.
2) 14 playable characters, 20 assist characters. I'm not sure about beginner characters, though Saber and Ruili seem to be pretty easy to pick up and play, but I'm not entirely sure. Characters you probably shouldn't play if you're unsure are Sonico and Saya. Luckily, if you're not sure which assists to choose, the game has recommendations for each character.
3) 1v1 matches. You pick your character and 2 assists who can be called in with a single button. General combat controls are as follows:
- 4 attack buttons: Light, Medium, Heavy, and Heavy Action (seems to be the launch, but again, I'm not sure)
- A dodge button of sorts, can be used to get behind your enemy or shield against attacks if you hold back when pressing it
- A burst that cancels your current move, knocks your opponent in a certain direction depending on the direction you're holding, and for a short time refills your health and special bars
- Everyone has a super attack a la Guilty Gear/BlazBlue that drains your whole special meter, but it doesn't get rid of it for the rest of the round
Special meters are divided into 3 segments, and there are mechanics other than just supers to drain it. Online is also really smooth, in the matches I've played, almost all of them had no input lag and minimal slowdown. No 2 characters have the same fighting style, so there's a lot of different ways to play depending on what you want to try.
4) There aren't really any mechanics I would call unique to the game, it just blends the best elements of other fighting games and executes them wonderfully. Some of the assists are pretty cool, and I don't think I've seen moves like those in other fighters (some of them can even hurt/benefit both sides). Think of it like Dragon Quest VIII (if you've played it), it doesn't innovate, but it does take what works about fighting games and polishes them wonderfully, just a damn fine game. It seems to be compatible with most controllers/fightsticks, but I don't entirely know (I have my trusty 360 controller).