You definitely want this potential issue resolved before you buy the house. To answer your questions in order:
1. Yes, your tax assessment almost certainly will be reassessed. This does not mean they will automatically go up, but chances are they will. Put an inquiry in with the local tax assessor's office.
2. That could be a potential outcome. The conversion really should not have been made from garage to living room without the approval in place. There could be penalties as well.
3. Make the sale contingent upon the seller obtaining approval on the conversion. If you close on the house without these issues sorted out you could be held liable. Talk this over with your attorney: They will provide you with the legal protection and information you need. Remember, this is not meant as legal advice as only your attorney can provide you with such.
Jacobus "Jack" Vollenberg
RE Appraiser - Vollenberg Appraisers
Realtor/REO Asset Manager - ERA Statewide Realty
Office (908) 968-0336
Cell (973) 590-0142