Without being punished in any way from BoS side and Institute?
At the end I'll probably choose Instutite or Brotherhood side but I want to do some quests for the Railroad, but im a little afraid it's gonna return to my by synths being hostile again or something.

Yeah, you can join the Railroad but I think it has to be before infiltrating the Institute.

You can join every faction and are encouraged to do by each other.

They all think you're infiltrating the others, though.

Okay thanks one last question. If I do some quests for Railroad and kill the synths on the way- Will Synths still be friendly to me? (I've already been in the Institute)

Because I was doing that quest for em with Deacon (donut shop), and I didn't want to kill synths so I just waited for him to kill them himself xD

I think you can kill as many as you want.