Explain the origin of the Imam Mahdi?

The Holy Prophet (S) said,

"Al Mahdi is from us, Ahlul Bayt."1

The Holy Prophet (S) said,

"Certainly, Ali Ibne Abi Talib Alaihis salaam is the Imam of my ummat and my vicegerant upon them after me. And of his sons is Al Qaem, Al Montazar. One, through whom Allah will fill the earth will justice and equity like it would have been filled with injustice and tyranny."2

"Al Mahdi is from the sons of Fatima."3

Huzaifa says The Holy Prophet (S) has said,

"Even if one day remains for this world (to come to an end) Allah will prolong that day until he sends a man from my progeny (sons). His name shall be (like) my name." Salman asked, "From which of your sons, O Prophet of Allah?"He (S) replied, "From this son of mine", and thumped his hands upon Husain (as)"4

A Jew, named Nathal asked the Holy Prophet (S), "Inform me as to who is your successor? Because every Prophet had a successor and our Prophet Musa Ibne Imran (as) had designated Yusha Bin Nun as his successor."

The Holy Prophet (S) replied, "Yes my Vasi and the caliph after me is Ali bin Abi Talib and after him my grandsons Hasan and Husain, followed by nine of the offsprings of Husain. They are the holy Imams."

The Jew said, "O Muhammad, tell me their names."

'Yes,' said the Prophet (S), "When Husain will pass away, then his son Ali, and after Ali his son Muhammad and after Muhammad his son Jafar and after Jafar his son Musa and after Musa his son Ali and after Ali, his son Muhammad and after Muhammad his son Ali after Ali his son Hasan and after Hasan his son Hujjat Ibnul Hasan. These are the twelve Imams. Their number is equal to the chiefs of Bani Israel"5

    1.
    Sunan Ibne Majah .VoL2 Pg.23, Al Mustadrak Vol. 4 Pg. 557.
    2.
    Kamaaluddin Vol.1 Pg.288; Faraidus simtain Vol.2 Pg. 335-336.
    3.
    Sunan Ibne Majah Vol.2 Pg.24.
    4.
    Zakhaerul Uqba Pg.136 & 137: Faraidus Simtain Vol.2 Pg. 326.
    5.
    Faraidus Simtain Vol.2 Pg.133, Kifayatul Asar Pg.13 & 14. Yanabiul Mawaddah Pg. 441.