Can the promoter go to any other civil court against any order issued by RERA or the Appellate Tribunal?

No. RERA bars any civil court to hear & try any matter or issue any STAY order, in respect of any matter for which powers are vested with the RERA Authority or the Tribunal. However, one can always approach the High Court with a Writ Petition under article 226 of the Indian Constitution, since the High Court is not a civil court but a constitutional court.