A much better translation. The dialogue makes sense now. The reason for Hanji shaking that assholes hand was to check it for cuts from punching Nick. Historia's father gave her a different last name from himself in order to save her life.
Either Historia or her father must have been under constant surveillance the whole time for those guys to have showed up out of the blue like that. I wonder if the powers behind the scenes were perhaps expecting her to do something, and if it has any relation to Eren's ability. I believe Eren's father might be part of that group, and that for him to give Eren his current powers via an injection there must have been prototype test subjects before him...hint hint.