Can I get addicted to the mysterious serum?
The Fallout Wiki says that you cannot get addicted to it (under the picture).
Also, under the notes section:
Though the in-game consumable is not addictive for the player character, the Cabot family are psychologically addicted.
For the Nick Valentine part of your question, see this answer. He shouldn't permanently hate you for doing that (there is no mentioning of it on the Wiki pages), but his affinity will drop.