Masjid al-Aqsa cannot be the Far Mosque, can it?

TIMELINE

958-951 BC Solomon's Temple built
587 BC Solomon's Temple destroyed by Nebuchadnezzar's Babylonian armies
37-34 BC Second Temple built (King Herod)
70 AD Second Temple destroyed by General Titus and his Roman soldiers
572 AD Muhammad born
622 AD Muhammad's "night journey" and mir'aj
632 AD Muhammad dies
638 AD Muslim jihadists conquer Jerusalem, taking it from the Byzantines
688-691 AD Dome of the Rock built by Amir Abd-ul-Malik
715 AD Masjid al-Aqsa built by the Ummayads
QUESTIONS FOR DR JAMAL BADAWI (or any other Muslim)

In light of these dates:-

What Temple did Muhammad visit, enter and pray at, before ascending to heaven?

Seeing that the Qur'an mentions a journey of Muhammad's to a mosque that did not exist during his lifetime, how can Surah 17:001 possibly have it, and Muhammad, In Jerusalem???