Legal Question in Real Estate Law in California

No

No. Permitting is between the owner and the relevant government authority. Not between the owner and the tenant. Think of it this way: If you rent a car and the registration had expired on it, do you think you would not owe for the rental? Of course you owe for the rental. The rental company owes a penalty for failure to register the car, but you don't get out of paying to use it. The only way a tenant is excused from paying rent is if there is a government finding that it is not legally habitable due to major defects in its condition, such as holes in the roof or walls, no heat, or no running water.

Well, technically, you could file and serve a cross-complaint (which is probably what you mean by "counter-sue"), or you could raise the unpermitted-conversion issue as a defense. However, unless you were defrauded by the landlord and sustained actual damages as a result, I'd say the lack of permits is neither a basis for a successful cross-complaint nor of much relevance as a defense. The suit is probably in small claims court, right? Be sure to appear for the hearing, and I'd suggest reading up on small-claims rules and procedures beforehand. Try the Nolo Press book on California small claims.