You may clean your false ceiling self but my per personal advice it to hire professional cleaner because false ceiling cleaning depends types of False Ceiling, different materials require different cleaning methods like for mineral fiber, use a soft duster or vacuum, for gypsum, use a dry cloth or slightly dampened microfiber cloth for stains and for PVC ceilings can be cleaned with a damp microfiber cloth and mild detergent. Avoid harsh chemicals and ensure the ceiling is completely dry before turning on lights or fans.