1. My question is: who will enter Paradise after Profet Mohammed, sallallaahu 'alayhi wa sallam?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

A hadeeth was narrated in this regard; however, scholars held different opinions on its authenticity. Abu Hurayrah narrated that the Prophet, sallallaahu ʻalayhi wa sallam, said, “Jibreel (Archangel Gabriel) came to me, took me by the hand and showed me the gate of Paradise through which my nation (Muslims) will enter.” Abu Bakr said, “O Messenger of Allaah! I wish I had been with you so that I would have looked at it.” The Messenger of Allaah, sallallaahu ʻalayhi wa sallam, said, “You, Abu Bakr, will be the first of my nation to enter Paradise.” [Narrated by Abu Daawood]

Al-Haakim also narrated this hadeeth and classified it as saheeh (sound) according to the conditions of Al-Bukhari and Muslim. Ath-Thahabi agreed with Al-Haakim that it saheeh; but Al-Albaani classified it as dha'eef (weak).

Another narration was cited in this regard on the authority of Ali ibn Abi Taalib ; it says that Abu Bakr and 'Umar will be the first of the Muslims to enter Paradise. However, this narration is weak. It was cited by Al-ʻUqayli in his book Adh-Dhuʻafaa'. It reads, “The first to enter Paradise from this nation will be Abu Bakr and ʻUmar. I and Muʻaawiyyah shall be retained for reckoning.” Al-Haafith Ibn Hajar wrote, “This narration should be listed in the books on false and fabricated reports. It was cited by Al-ʻUqayli, who said that its narrator is unknown and his narration is not accurate...” [Lisaan Al-Meezaan]

Allaah knows best.