Dear Brother As'salaamu alaikum va rahmatullahi va barakatuhu,
Q 1- I want knows about first job of the Prophet Mohammad S. Business or as an Employee?
Q 2- What is better between Business and Employee?
Q 3- If any Muslim people hang according to Muslim law, will he go to Jannnat?

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 ‘alayhi wa sallam, is His slave and Messenger.

The Prophet said: “Allaah did not send any prophet except that he shepherded sheep”. The Companions asked, “Did you do the same?” The Prophet replied: “Yes, I used to shepherd the sheep of the people of Makkah for some Qiraat (gold or silver currency).” [Al-Bukhari]

We do not know any narration that proves that he had engaged in any job before this work.

However, he traveled to Ancient Syria during his youth as a trader while he was a business partner with Khadeejah as mentioned by Imaam Ibn Hajar .

As for what is preferable; running a business or being employed, then the Muslim jurists have many opinions concerning the best earnings whether it is agriculture, trade, manufacturing or employment, and there is no text giving preference to one over the others.

With regard to whether or not a person who is killed according to the Islamic law (as a penalty for a crime he committed) enters Paradise, then killing him is an expiation for that sin because when the Prophet took allegiance from his Companions, he warned them against fornication/adultery, killing innocent people, etc and then said: “… and whoever is involved in such things and gets its punishment in this world, then it will be an expiation for him.” [Muslim] See Fatwa: 87760.

The scholars, like At-Tahaawi said that other sins are subject to the Will of Allaah; He may forgive the sins or He may punish for them. This principle applies to every Muslim who dies believing in the Oneness of Allaah. Even if one is punished for his sins then in the end he will enter Paradise for his faith, Allaah willing.

For details see Fataawa 89470 and 82281.

Allaah Knows best.