From some quick internet research, Danny does not necessarily have to give the thumb drive to the FBI since Alden gave it to him specifically as an NYPD Detective.
First, let me know if I'm wrong on this because I have no background in this and only did some half-assed internet research. It looks like as an NYPD officer, Danny is not necessarily legally required to hand over that evidence to the FBI. He is the lead detective on the Easton murder and this is evidence that is relevant to his case. Alden specifically only gave that information to him because he could sense, like we all can, that Danny is worth trusting.
I think he will only tell Alice, who will only tell Nora. And I think the 3 of them are going to work this case together with this new information and keep everyone else out of it. I think they will stall on handing this evidence to the FBI as long as possible. With Ed trying to take over, the evidence is truly not safe in the hands of the FBI. It also seems like it would be easy for the FBI to quietly get rid of both Nora and Alice - Nora for drinking and Alice for pulling a gun on her boyfriend - unless they are the ones to get Catherine and take down the Easton family. That success would keep their jobs safe.
Do you think he would let Alice delete her video and do you think she would? It probably wouldn't help her career and she would be a part of the child pornography database at the FBI for the rest of her life. I think if she wanted to erase it, he would let her. Anyone who cares about anyone would probably do the same.
Also, shout out to - and I wish I could find the comment - the person who called this. Someone on this sub said the way she looked at the door of the child pornography room probably meant she was in a video. What a catch of a minor detail and amazing acting from Emmy.