Her spectre was captured and used to lure her right? What happened in the end? Does she get her spectre back? Or do I just keep watching to find out? What exactly does capturing a spectre do?
It's returned to her at the end of the episode. to quote Episode 13/14 on the Wikia
Itzhak tries to make a run for the car, but he gets shot in the back by Huang with a sniper rifle. Huang then aims for Yin, however he notices first that the dying Itzhak has started to glow. Itzhak begins emanating outward all the surveillance spectres that he took in, and they soon cover the sky in a beautiful swirl. In his final words, Itzhak tells Berta that this is the light of the moon, a moon filling in silvery white. Both Hei and Huang are shocked to see Yin crying, and although Huang still takes aim, he can’t pull the trigger.
It's implied that she got her Spectre back as in future episodes we also see Yin's Spectre
in Without Dreaming Shallow Dreams, and Falling Drunk... Huang has Yin use her spectre to keep an eye on Hei and Shihoko which blows their cover and exposes Shihoko as traitor to Alma's organization.
in The City of Regulations Is Moistened by Tears... Yin's spectre appears in Mao's water dish when Hei, Yin and Huang go to rescue Mao who ended up in Evening Primrose hideout
Also Yin's Spectre makes appearances in Gemini of the Meteor as she tried to reach out to Hei
however Hei has lost his Contractor Powers to the Meteor Core Suou wears and only Suou sees her evolved specter appear from puddles
As for what capturing a Spectre does the Dolls seem to become "lost" without their Spectre
he then notices another surveillance spectre - one belonging to Yin - out on the water and tries to suck it up too. His action causes Yin to suddenly fall down in the dark alley where she’s standing ... In a hotel room somewhere, the Contractor whose name is Itzhak tells the fat woman Berta that the Doll he shocked last night is adrift somewhere as if sleepwalking.
there is also the lost of their observational power, however aside from this there is little to go on as most Dolls used for observation are normally kept confined like the ones used by Evening Primrose during their attack on Hell's Gate or the National Astronomical Observatory of Japan and all of these seem to be without wills similar to how Sakurai was originally. the only 4 who seem to have "wills" and have Spectres are Yin, July and Ariel and Bernice.