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This is Ann Weying, Eddie's ex-wife, played by Michelle Williams. In the comics, she's a lawyer, although it's been strongly implied that she works alongside the Life Foundation in the movie, perhaps even arranging Eddie's interview with Carlton Drake at the beginning of the film. Here, Eddie begins to talk to Ann about the power he's gained through exposure to the Venom symbiote. In a subsequent shot, he swiftly demonstrates that this power can be used for good, protecting her from a hail of gunfire. Given the effect a symbiote has on a person, it's no surprise that Eddie's comments scare Ann a great deal.
In the comics, Venom is well-known for scaling walls just like Spider-Man; in fact, his symbiote typically forms a web-line too, in honor of its first human host. Given Venom's backstory has been rewritten for the movie, it's no surprise the web-lines appear to have been cut, although wall-crawling is still evidently a part of her powerset. The speed and agility with which Venom moves shows the film isn't holding back; he may be a hulking beast, but that doesn't mean he isn't swift on his feet.
One short sequence spliced into the trailer shows an ambulance speeding down a road, flipping over when the driver is attacked from behind by a symbiote. Based on the content of other scenes, it seems likely the ambulance was taking someone to hospital who'd been exposed to a symbiote (going by the silver and red color of the tendrils, Riot) at the crash site.
In this scene, from the clothing evidently set in China, an EMTS who's been exposed to the Scream symbiote goes on something of a killing spree. This looks to be the beginning of her onslaught, with the symbiote forming a bladed weapon with which to slash a throat. The trailer revisits this scene a few moments later, showing the symbiote project a salvo of blades from its back - to lethal effect. In the comics, that particular method of attack is similar to one deployed by a member of the Five Symbiotes, Lasher. The Lasher symbiote manifests weapons from its back, particularly whips (hence the name).
It appears to be Scream who ultimately infects Eddie, so she's presumably then captured by the Life Foundation. It would explain where Drake got the idea of bonding humans to symbiotes from; it had already happened once before, albeit in an uncontrolled environment.
Eddie may not want to hurt innocent people, but what can he do when innocent people come looking for him? In this case, Eddie has been hunted down by an entire SWAT team - and it's not hard to deduce what will happen next.
In terms of the film's overall plot, this scene suggests that Eddie's antihero identity becomes known to the authorities. Even if Eddie defeats the Life Foundation, it's quite possible he'll be a wanted man by the end of the movie.