I'm working for the Railroad, and have some questions about quests given to me by Maxson.

One of them is having to give a tape to someone at the Airport below the Prydwen. If I'm infiltrating the BoS, does giving this tape help me find a weakness against the Institute? Because it kind of feels like actually working for the BoS and that's not what I want. Also, Piper liked me giving the tape to them (or she like my response?). I don't get that, she didn't like when I joined?

The other question is about getting Dr. Li back to the BoS. Does anyone know what she wants herself? I have a feeling I'm going to have to kill her in the end if I send her back there, as the BoS will ultimately brand me an enemy.

Edit: Not sure I want her back at the BoS if it means they'll have her fix Liberty Prime. Not an enemy I'd like

Also, will any of these quests get me in trouble with the Railroad?

Thanks in advance for any help/replies

Edit: Will helping the number of synths in the Institute (Railroad quest) get me in trouble with the Railroad?
I believe it's a very clear point when you'll actually have to chose, but I'm just checking.