Did Prophet Mohammed saw Jerusalem Temple? Is the Al-Aqsa mosque built on ruins of Jerusalem Temple?

Did Mohammed ever see the Jerusalem Temple?

No, Mohammed never saw the Jerusalem Temple as it was demolished by the Romans 500 years before Mohammed's birth.

Mohammed was born in AD 570 in Mecca. He began preaching Islam in AD 610 and continued until his death in AD 632. Therefore, he could not have seen the Jerusalem Temple, which was destroyed long before his birth. However, he might have heard about it from Jewish inhabitants in Arabia. 

Al-buraq, the winged
horse of Mohammed

Mohammed never made a physical visit to Jerusalem

In fact, Mohammed never made a physical visit to Jerusalem. However, he claimed to have experienced a spiritual journey, possibly a dream or vision, in which he traveled from the Kaaba in Mecca to the "Farthest Mosque." Muslims believe this mosque to be the Al-Aqsa Mosque in Jerusalem. According to the tradition, he made this journey on a winged, horselike creature known as Buraq.

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Was the Al-Aqsa mosque built on the ruins of the Jerusalem Temple?

Yes.

The Jerusalem Temple was demolished by the Romans years before Mohammed's time. Vespasian was declared Emperor of Rome on July 1, AD 69. His son, Titus, was sent to the province of Palestine to suppress the Jewish rebellion against the Roman Empire. In AD 70, Titus' army plundered Jerusalem and demolished the Temple, leaving only the Western Wall, also known as the Wailing Wall.

After Mohammed’s death in AD 632, during the reign of fifth Umayyad caliph Abd al-Malik ( AD 685–705) and his successor al-Walid I ( AD 705–715) under the Islamic invasion of the Palestine region, Muslims ,  built the Al-Aqsa mosque between AD 685 and 715 on the site of the demolished Jerusalem Temple.