Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Believing in angel is a fundamental of Islamic creed. Nobody can be a believer unless they believe in Angels. Allah says: "The Messenger (Muhammad) believes in what has been sent down to him from his Lord, and (so do) the believers. Each one believes in Allâh, His Angels, His Books, and His Messengers. They say, "We make no distinction between one another of His Messengers" (Al-Baqarah 2:285)
The Prophet (Sallallahu Alaihi wa Sallam) said: "Iman (belief) is to believe in Allah, His Angels, His Books, His Messengers and to believe in Destiny be it good or bad."
Following are the 5 tenets of believing in Angels.
1. "They (i.e. the angels) glorify His Praises night and day, (and) they never slacken (to do so). (Al-Anbiya 21:20)
2. "They disobey not, (from executing) the Commands they receive from Allâh, but do that which they are commanded. (At-Tahrim 66:6).
3. "They cannot intercede except for him with whom He is pleased. And they stand in awe for fear of Him. (Al-Anbiya 21:28)
4. "He (Allah) made the angels messengers with wings, - two or three or four. He increases in creation what He wills. Verily, Allâh is Able to do all things." (Fatir 35:1)
5. That angels "were created from light" as reported by Imam Muslim.
As for the second question, Al-Bukhari reported in a Hadith narrated by Abu Hurairah that the Prophet (Sallallahu Alaihi wa Sallam) said: "All (members of) my Ummah will enter paradise except those who refuse (to enter it). They said: "And who will refuse?" He replied: "Whoever obeys me enters
For your third question, please read 82038
Allah knows best.