Did the Messenger of Allah (peace be upon him) say, "I and Ali ibn Abi Talib are the gate of this Ummah"? And is it permissible to marry a girl who follows a madhhab different from that of Ahl al-Sunnah?

The phrase you asked about, "I and Ali ibn Abi Talib are the door of this Ummah," was not reported. Rather, another wording was reported: "I am the city of knowledge and Ali is its gate; so whoever desires knowledge, let him come through the gate." Al-Albani and Ibn Taymiyyah judged this narration to be fabricated, as Ibn Taymiyyah believed that the falsehood of the hadith is evident from its text, for it is not permissible for the one who conveys knowledge from the Prophet, peace and blessings be upon him, to be only one person.