Hadith regarding the Muslim Ummah

Q: Please enlighten me with the references of this hadith: Conjoined Hadiths from Musnad Ahmad: Jaabir (radhi-yallaahu 'anhu) narrated that Allaah's Messenger (sal-Allaahu`alayhe wa sallam) said: "Al Muslimoon Ummatun Wahida, Wa Biladahum Wahida, Wa Harbahum Wahida, Wa Salmahum Wahida". Is this a Hadith at all?

Hadith regarding perfect Imaan

Q:

  1. I read that no one will enter jannah unless they have perfect imaan. So if a person has Imaan but it is not perfect will he attain jannah? Quote hadith or quraan ayaats if possible.
  2. What is perfect imaan? If I commit a sin does it mean I do not have perfect imaan ?
  3. Can you send me the hadith which says how one can attain perfect imaan through salaam?

Hadith regarding securing a house in Jannah

Q: Is the following hadith authentic and in the proper wording ?

Umm Habibah bint Abu Sufyan reports that the Messenger of Allah (Sallaho Alaihe Wassallam) said: "Whoever prays twelve rak'at during the day and night will have a house built for him in paradise: four rak'at before zuhr and two after it, two rak'at after maghrib, two rak'at after 'isha, and two rak'at before fajr." (Tirmidhi, who graded it as Hasan sahih).

Can you send me any more hadith that says how to get a house in jannah?