2) "...Secondly tha hadeeth of Ayisha quoted above has nothing to do with taraweeh..."

hadeeth of Abu Salamah ibn ‘Abd al-Rahmaan, who asked ‘Aa’ishah (may Allaah be pleased with her), “How did the Messenger of Allaah (peace and blessings of Allaah be upon him) pray during Ramadaan?” She said: “He did not pray more than eleven rak’ahs in Ramadaan or at other times. He would pray four, and do not ask how beautiful and long they were, then he would pray four, and do not ask how beautiful and long they were, then he would pray three. I said, ‘O Messenger of Allaah, will you sleep before you pray Witr?’ He said, ‘O ‘Aa’ishah, my eyes sleep but my heart does not.’”

Narrated by al-Bukhaari, 1909; Muslim, 738

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Taraweeh and tahajjud are one prayer - for this also i have provided the reference in previous posts.

Also the same is proven from following narration:

jaabir Ibn 'Abdullah agreed with 'Aa'ishah, he said: " When the Prophet prayed with the people one night during Ramadaan he prayed eight raka'at and then made Witr." [Ibn Hibbaan].

So it is beyond any shade of doubt that 8 rakats is what is proven from sunnah.