Yes. Imams often and regularly break up surat similarly when reciting in tarawih.

To my knowledge, the general ruling for reciting during salat (after reciting al-Fatihah) is that it should be at least three ayat, but there's no requirement that the recitation makes up a complete surah.

Yes. Imams often and regularly break up surat similarly when reciting in tarawih.

Generally, only al-Fatihah is considered strictly necessary when reciting fard salat; beyond that you may recite from the Qur'an however is easy for you.

To my knowledge, the general ruling for any recitation after al-Fatihah is that it should be at least three ayat, but there's no requirement that this recitation needs make up a complete surah.