The idea is interesting. I do like it, and I think the core concept of having different effects and making her more reliant on the effects of her passive is a good idea. It's overall a pretty nice rework concept. I just want to make it clear that I do like it, even though I'm about to spend time focusing mainly on the few problems that I have.
First off, while I do think the passive sounds pretty interesting, I think that the large disparity in the effects Annie can get would actually feel a bit limiting to the players when combined with her cooldowns and the large number of stacks needed. There are going to be situations where I really, really want to get certain effects (largely the stun, and rarely but sometimes the movement speed), but I'll have to sit on long cooldowns to actually achieve them, and the 7 stacks will be up rarely enough that this may be punishing. I'll have to wait on an important cooldown for a long time to make sure I can use it with the bonus effect. Redesigning her Q to be spammier (lower damage, CD and manacost) to help build up stacks easily while in range of an enemy might be a workable solution. Having a low duration but low CD E could work too, although I'm not sure if that really fits her design. This problem probably isn't particularly hard to address.
The Q pyromanic design seems kind of odd to me. I'm not sure about the idea of having her Q someone to apply a permaslow and DoT so long as she isn't CCed. Seems a bit odd, and potentially unfair. What is the idea you're going for here? I could see the idea of having her slow people down for the bear to chase them, but my objection there would be that a Rylai's on the Tibbers aura is going to do that anyway. I'm just not sure what exactly the point of having this is. I don't really know what you'd put here, but I do think that something else needs to fill this slot.
I'd also argue that having Tibbers stun is still going to be pretty important to her kit, and should probably be included in the ability. A lot of her utility her is based on a teamfight stun, and given that there will be less immediate burst, fewer stuns from her passive, and the bear will be dodgeable, I'd say that she's really, really going to need that stun.
Aside from all that, the concept is pretty interesting. I like having different effects on her abilities, I like the E being a more useful part of her kit and it does seem a lot more fair to play against in general. Pretty good job.