Apparatus and methods for denitrification and desulfurization of and dust removal from an FCC tail gas by an ammonia-based process. The apparatus may include a first-stage waste heat recovery system, a denitrification system, a dust removal and desulfurization system, a tail gas exhaust system, and an ammonium sulfate post-processing system. The dust removal and desulfurization system may include a dedusting tower and an absorption tower disposed separately. The top and the bottom of the absorption tower may be connected respectively to the tail gas exhaust system and the ammonium sulfate post-processing system. The absorption tower may include sequentially, from bottom to top, an oxidation section, an absorption section, and a fine particulate control section. The methods may be implemented with the apparatus.