Only Muslim fighters will get the big rewards

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Orders given by Muhammad to the people who would run things after he died.
Sahi Al Bukhari Vol 4.386:
Narrated Jubair bin Haiya: `Umar sent the Muslims to the great countries to fight the pagans. When Al−Hurmuzan embraced Islam, `Umar said to him. "I would like to consult you regarding these countries which I intend to invade." Al−Hurmuzan said, "Yes, the example of these countries and their inhabitants who are the enemies. of the Muslims, is like a bird with a head, two wings and two legs; If one of its wings got broken, it would get up over its two legs, with one wing and the head; and if the other wing got broken, it would get up with two legs and a head, but if its head got destroyed, then the two legs, two wings and the head would become useless. The head stands for Khosrau, and one wing stands for Caesar and the other wing stands for Faris. So, order the Muslims to go towards Khosrau." So, `Umar sent us (to Khosrau) appointing An−Nu`man bin Muqrin as our commander. When we reached the land of the enemy, the representative of Khosrau came out with forty−thousand warriors, and an interpreter got up saying, "Let one of you talk to me!" Al−Mughira replied, "Ask whatever you wish." The other asked, "Who are you?" Al−Mughira replied, "We are some people from the Arabs; we led a hard, miserable, disastrous life: we used to suck the hides and the date stones from hunger; we used to wear clothes made up of fur of camels and hair of goats, and to worship trees and stones. While we were in this state, the Lord of the Heavens and the Earths, Elevated is His Remembrance and Majestic is His Highness, sent to us from among ourselves a Prophet whose father and mother are known to us. Our Prophet, the Messenger of our Lord, has ordered us to fight you till you worship Allah Alone or give Jizya (i.e. tribute); and our Prophet has informed us that our Lord says:−− "Whoever amongst us is killed (i.e. martyred), shall go to Paradise to lead such a luxurious life as he has never seen, and whoever amongst us remain alive, shall become your master." (Al−Mughira, then blamed An−Nu`man for delaying the attack and) An−Nu' man said to Al−Mughira, "If you had participated in a similar battle, in the company of Allah's Apostle he would not have blamed you for waiting, nor would he have disgraced you. But I accompanied Allah's Apostle in many battles and it was his custom that if he did not fight early by daytime, he would wait till the wind had started blowing and the time for the prayer was due (i.e. after midday).

Chapter 31: THE HIGH POSITION RESERVED BY GOD FOR MUJAHIDS IN PARADISE
Sahi Muslim Bk 20, Number 4645:
It has been narrated on the authority of Abu Sa'id Khudri that the Messenger of Allah (may peace be upon him) said (to him): Abu Sa'id, whoever cheerfully accepts Allah as his Lord, Islam as his religion and Mubammad as his Apostle is necessarily entitled to enter Paradise. He (Abu Sa'id) wondered at it and said: Messenger of Allah, repeat it for me. He (the Messenger of Allah) did that and said: There is another act which elevates the position of a man in Paradise to a grade one hundred (higher), and the elevation between one grade and the other is equal to the height of the heaven from the earth. He (Abu Sa'id) said: What is that act? He replied: Jihad in the way of Allah! Jihad in the way of Allah!

Chapter 28: THE MERIT OF JIHAD AND CAMPAIGNING IN THE WAY OF ALLAH
Sahi Muslim Bk 20, Number 4626:
It has been narrated on the authority of Abu Huraira that the Messenger of Allah (may peace upon him) said: Allah has undertaken to look after the affairs of one who goes out to fight in His way believing in Him and affirming the truth of His Apostles. He is committed to His care that Re will either admit him to Paradise or bring him back to his home from where he set out with a reward or (his share of) booty. By the Being in Whose Hand is the life of Muhammad. If a person gets wounded in the way of Allah, he will come on the Day of Judgment with his wound in the same condition as it was when it was first inflicted; its colour being the colour of blood but its smell will be the smell of musk. By, the Being in Whose Hand is Muhammad's life, if it were not to be too hard upon the Muslime. I would not lag behind any expedition which is going to fight in the cause of Allah. But I do not have abundant means to provide them (the Mujahids) with riding beasts, nor have they (i. e. all of them) abundant means (to provide themselves with all the means of Jihad) so that they could he left behind. By the Being in Whose Hand is Mubammgls lac, I love to fight in the way of Allah and be killed, to fight and again be killed and to fight again and be killed.

Chapter 32: ONE WHO IS KILLED IN THE WAY OF ALLAH WILL HAVE ALL HIS SINS BLOTTED OUT EXCEPF DEBT
Sahi Muslim Bk 20, Number 4646:
It has been narrated on the authority of Abu Qatada that the Messenger of Allah (may peace be upon him) stood up among them (his Companions) to deliver his sermon in which he told them that Jihad in the way of Allah and belief in Allah (with all His Attributes) are the most meritorious of acts. A man stood up and said: Messenger of Allah, do you think that if I am killed in the way of Allah, my sins will be blotted out from me? The Messenger of Allah (may peace be upon him) said: Yes, in case you are killed in the way of Allah and you were patient and sincere and you always fought facing the enemy, never turming your back upon him. Then he added: What have you said (now)? (Wishing to have further assurance from him for his satisfaction), he asked (again): Do you think if I am killed in the way of Allah, all my sins will be obliterated from me? The Messenger of Allah (may peace be upon him) said: Yes, it you were patient and sincere and always fought facing the enemy and never turning your back upon him, (all your lapses would be forgiven) except debt. Gabriel has told me this.

Fighter convinced by Muhammad to fight to his death to gain paradise
Sahi Muslim Bk 20, Number 4678:
It has been reported on the authority of Jabir that a man said: Messenger of Allah, where shall I be if I am killed? He replied: In Paradise. The man threw away the dates he had in his hand and fought until he was killed (i. e. he did not wait until he could finish the dates). In the version of the tradition narrated by Suwaid we have the words:" A man said to the Holy Prophet (may peace be upon him). on the day of Uhud......"

Man becomes a Muslim and fights then dies on the same day, but will get a great reward if Islam is true.
Sahi Muslim Bk 20, Number 4679:
It has been reported on the authority of Bara! ' who stated: A man from Banu Nabit (one of the Ansar tribes) came to the Holy Prophet (may peace be upon him) and said: I testify that there is no god except Allah and that thou art His bondman and Messenger. Then he went forward and fought until he was killed. The Holy Prophet (may peace be upon him) said: He has done a little but shall be given a great reward.

Chapter 47: DENUNCIATION OF ONE WHO DIED BUT NEVER FOUGHT IN THE WAY OF ALLAH NOR DID HE EVER EXPRESS A DESIRE OR DETERMINATION FOR JIHAD
Sahi Muslim Bk 20, Number 4696:
It has been narrated on the authority of Abu Huraira that the Messenger of Allah (may peace be upon him) said: One who died but did not fight in the way of Allah nor did he express any desire (or determination) for Jihid died the death of a hypocrite. 'Abdullah b. Mubarak said: We think the hadith pertained to the time of the Messenger of Allah (may peace be upon him).