I was debating whether to get Lucian since I saved enough IP, but held off for a while since I read about the leak; glad I didn't buy him now (especially since it looks like more Lucian nerfs are incoming; Q range is probably getting reduced next patch). Going loosely off your talking points:
Her uniqueness is pretty apparently in her ult, imo; her passive lets her move pretty similarly to Vayne, her Q is a pretty standard line skillshot, though it bears a lot of resemblance to Nidalee's spear, if only due to the fact that it's also a spear; it also gives her a free short ranged dash due to her passive. Her W functions like a lot of other ADC's vision abilities, but also has the passive element where it deals bonus damage if your soulbound attacks the same target. Her E feels a lot like Twitch's expunge. Her ult lets you Syndra-grab a pre-determined teammate and lets them dash to the front lines with a huge CC effect, and that's awesome.
Kalista looks like an incredibly powerful champion in the right hands and with a good team, but is probably pretty risky in solo-q. I don't think she's OP out of the gate; this is without knowing any of her stats or cooldowns, but they have areas where they can certainly tune her if necessary. Her E seems like the focal point of her damage, I'm assuming BotRK first buy; generally a Vayne/Twitch style build. Generally she seems a lot like Vayne with more utility and less raw hypercarry/solo ability; she seems a lot more team focused, a lot more defensive (her passive makes her dash further if she's going away from an enemy, conversely it's fairly short range going towards the enemy. You'll probably still be able to chase an enemy indefinitely if you have enough attack speed, good mechanics, and they don't have a longer range dash or jump so you can't reset your passive; at the same time it seems that you can go further by moving in a zig-zag, which will make it easier to kite or chase). In a lot of ways, she seems like the champion that Ashe should be/needs to be to keep up at the highest tiers; she has a huge CC ult, great kiting potential, and vision control/utility.
Weaknesses seem to be reliance on her team; she does better with specifically her soulbound teammate. Will have to wait for more info to confirm, but it seems like short range might also be a weakness; they mention she doesn't have massive range, not sure if they mean Kog'Maw/Tristana massive range, or they mean she actually has lower AA range than most ADCs (I'd assume it's the average 550). Judging from the reveal, some other weaknesses seem to be a slow attack animation (from what they said about Zyra countering her; another reason why AS is probably going to be prioritized), and less mobility outside of fights/vulnerability to hard engages. If these are actually supposed to be weaknesses, they might need to be further emphasized, based on what I've seen from the videos; although she doesn't have a standalone mobility spell, Q+Passive+E slow seems to be just about as good at creating distance from a single target as most other ADC mobility abilities (ie. Ezreal, Lucian, Graves, Caitlyn). She also doesn't seem like a lane bully; not a weak laner by any means, but bullying seems to depend on the support synergy with the W passive; she's not Lucian who can just solo the other laner, or Caitlyn, who has crazy range and waveclear (another weakness; lack of waveclear).
Strengths seem to be any time she's with her soulbound, and also in teamfights. Her ult gives great initiation potential, or follow up CC if your team initiates without you (depending how long your teammate can stay in that state, it might be impractical to try to carry them around and look for a fight; it might be better if they engage and you can call them back so they can jump back in for follow-up CC or to peel for you). I feel like she's a more evened-out Vayne, where she isn't as weak early or mid game, but not as dominant late game. She has incredible mobility inside of fights and lane, where there are plenty of minions to auto.
To be continued
or 
. This is clearly demonstrated in the autoattack-hop passive, which consequently encourages building items like 
and/or 
to further increase the pre-existing chase built into her kit. The reason Kalista seems OP as of now is because of her massive potential to chase down a speedy opponent and the infinite stacks that can be placed on said opponent.
