1) Technically you could take someone to court without knowing their name
2) They could apply for a search warrant but the likelihood of one being granted is miniscule without decent evidence to give reasonable suspicion. This is a scare tactic.
3) Bear in mind you are under no obligation to give a statement if you don't feel you want to. It's very unlikely the police would ever get involved although this is a criminal offence not civil.
Have also heard that the police are generally reluctant to task a couple of offers with helping them execute search warrants too and if you're not in then they're unlikely to actually break the door down.
Though it does apparently happen on occasions.