I highly doubt Comey would do what he did unless they found something that may alter the course of the investigation. It just doesn't make sense otherwise, unless it was a maneuver to cover himself in case he's hailed back in front of congress for saying they had closed the investigation when in fact they have not.
I don't think he would do this just to influence the election. There are obviously a lot of rumors out there, but if any of them are true, it's horrible news for HRC.
Without a search warrant for Abedin's emails, it would be illegal to search them
Unless she or Weiner willingly handed them over, which is what some rumors are suggesting. We have no idea, but you're right about the warrant.
I expect the letter was just to cover his ass, but right now no one knows anything aside from the rumors being reported online.