Is it permissible for the Imam to reverse the order of the surahs in prayer by reciting part of Surah An-Nisa in the first rak'ah, and then part of Surah Al-Baqarah in the second rak'ah? And what is the evidence for that?

Reciting the surahs in reverse order during prayer is contrary to what isفضل (preferable/best), but the prayer is valid and there is no harm in it. It is preferable to recite the surahs according to the order of the Mus'haf, but if one deviates from that, there is no objection. Imam Ahmad and others have cited that the Prophet (peace be upon him) used to teach the Quran in this manner, and that the order of the surahs is a matter of ijtihad (scholarly discretion). As for reciting the verses in reverse order, it is forbidden because their arrangement is by textual evidence and consensus, and deviating from that alters the meaning.