Imamate was created by the enemies of Islam (Yahudi ibn Saba) to destroy Islam from the inside.
No - that would be
wasiyya. Meaning that Rasul Allah (saws) specifically designated 'Ali (ra) as his successor, and that 'Ali (ra) was infallible, divinely appointed, and that all those who reject this are kaffir.
Imamah in the Sunni sense is perfectly valid - and refers primarily to
khilafa. The
Khalif is the
Imam of the Muslims, elected through
shura (preferably).
Ok so much for Shia Imamate. Now coming to the main question which I have. I want to know from where did the concept of Khilafat arise i.e. Khilafat-ur-Rasulullah. Living in 21st century we don't have any present Khalifa and yet Islam is in existence then why did the need of Khalifa arise after the Prophet (s.a.w.w) left this world?
The need for a single person to lead the community is
fitra. Even if there was no specific textual basis for it, it would come naturally to most communities. Infact it did - the concept of a single person with authority over the affairs of the state is accepted by every civilization.
As for Islam - Rasul Allah (saws) did indeed mention
Imamah in the Sunni sense - namely that the Muslims need to unite around a single leader and give him
bay'a. These ahadith are found everywhere.
If the answer would be at that time Islam needed someone to look after the affairs of the Islamic State then why did Prophet (s.a.w.w) himself not nominated his successor to look after the State of Muslim affairs? Or if Prophet (s.a.w.w) did not nominate his successor then did he give the method on how to select his successor i.e. Khalifa / Ameer of Muslims?
Rasul Allah (saws) did not nominate a successor for several reasons:
1. The choice of his successor was obvious to everyone - Abu Bakr (ra).
2. He was a
nadhir (warner), not a
wakeel. His job was to teach the religion and then to leave. Appointing a successor completely nullifies this very basic Islamic article of faith.
Infact, the Qur'an makes zero reference to his successor in the sense of an individual. His true successor in the Qur'an is the Ummah (Qur'an 2:143), beginning with the Sahaba as a polity.
And lastly can we find any support or evidence for the concept of Khilafah in Al Qur'an or Sahih Hadiths? That is to say did Previous Prophets have any succesors e.g. Prophet Adam (a.s), Nuh (a.s), Ibrahim (a.s), Musa (a.s) and Isa (a.s)?
The previous messengers and prophets had divinely appointed successors - who were also messengers and prophets.
The final Prophet (saws) had no divinely appointed successor.