Is the prayer of one who intended to pray Maghrib behind an Imam praying 'Isha valid, then gave the salutation after three rak'ahs, then completed another rak'ah with the Imam, then completed a final rak'ah on his own, valid?

Your Maghrib prayer behind an Imam leading Isha is valid, and it is permissible for you to separate from the Imam after the third rak'ah. However, your shortening of the Isha prayer after following a resident Imam is not valid, due to the hadith narrated by Ibn Abbas: "That is the Sunnah of Abu Al-Qasim (peace be upon him)." You must repeat the Isha prayer as four rak'ahs.