Does the Quran order the killing of none believers?

I will now quote the last verse that Christians so famously quote to prove that Islam orders the killings non-believers. I will again past the verse exactly as it is stated on the Christian website;

Surah 9:5: “Then kill the disbelievers (non-Muslims) wherever you find them, capture them and besiege them, and lie in wait for them in each and every ambush …”

Of course any who reads this verse as is would think this is the case but I will now show you once more the deceit of these Christian writers.

Before I quote the verses let me give you some background so that you can understand the context and what the verses are referring too. 

Six years after Prophet Muhammad (pbuh) migrated to Madina three battles was fought against the pagan Makkans in which the Muslims were mostly victorious except one when they had to retreat due to the fact that certain soldiers guarding a certain hill protecting the Muslims from behind had disobeyed orders.

In 628 CE, the holy Prophet (peace be upon him) dreamt that he and his followers were entering Makkah and performing tawaf (the rounds around the Kaaba or pilgrimage). It was a good sign and hence he declared his plan to visit Makkah to perform Umrah.
Over 1,400 Muslims donned ihram (pilgrimage dress code) with him from Madinah. They took 70 camels with them for sacrifice. As per the established practice, the Makkans were bound to allow pilgrims coming — but without arms — to perform Umrah. But, alarmed by the huge Muslim presence, the Quraish leaders decided not to allow them from entering the city and sent Khaled Bin Walid with 200 fighters to stop them defying the centuries-old Arab tradition.

The holy Prophet (peace be upon him) changed the route of Taneem to avoid confrontation and came to a lesser-known place called Hudaibiyah on the western edge of the city.
Determined not to allow Muslims enter the city, Makkans sent Urwah bin Masud to negotiate with the Prophet. Highly impressed with the scenes of Prophet’s love among his followers, Urwah said, “I have visited the royal courts of the Persians, Roman and Ethiopian kingdoms, but I have never seen the kind of respect and high esteem as the followers of Mohammad have for him. They have come only for worship. Let them enter the holy city.” But the Makkan leaders were bent upon preventing the Muslims.
The holy Prophet (peace be upon him) later sent Uthman bin Affan who had good contacts in Makkah but they detained him and spread a rumor to upset the Muslims that Uthman has been killed. This was a great challenge. Though 400 km away from his city and having no proper arms to fight, he prepared for a war like situation and called his followers to prepare for fight unto death. The people rushed to take an oath of allegiance on his pious hand and within short time the news reached Makkah that 1400 volunteers were ready to fight unto death. This broke their morale and Makkans agreed to discuss terms of peace with him.
They released Uthman and sent Sohayl bin Amr Al-Thaqafi to negotiate the terms of peace with the Prophet Muhammad (peace be upon him). Sohayl (later embraced Islam) was very tough in dealings.  This was called the treaty of Hudaibiyah for which the term was ten years. 

As per the agreement, Banu Bakr tribe joined Al-Quraish and Banu Khaza’a entered into alliance with the Prophet. But they both had long history of enmity between them. Just after 20 months, Banu Bakr attacked Banu Khaza’a in Sha’ban, 8AH. They killed many Muslims and their chief, Nofel, did not spare them even inside the holy city. The Quraish also supported them with men and arms. Amr bin Salem of Banu Khaza’a with 20 men rushed to Madinah and advised the holy Prophet with real situation. The Prophet (peace be upon him) again rose high to the challenge. He sent a word to Quraish, pay ransom for the persons killed or terminate your alliance with Banu Bakr or treat the Hudaibiyah Treaty as abrogated. The Quraish arrogantly replied we shall neither pay ransom nor terminate our alliance with Banu Bakr but are ready to abrogate the treaty with you. 

This is when the verses of Surah At – Tawbah (9:1-5) was revealed to the Prophet Muhammad (pbuh);

(9:1) [This is a declaration of] disassociation, from Allah and His Messenger, to those with whom you had made a treaty among the polytheists.

(9:2) So travel freely, [O disbelievers], throughout the land [during] four months but know that you cannot cause failure to Allah and that Allah will disgrace the disbelievers.

(9:3) And [it is] an announcement from Allah and His Messenger to the people on the day of the greater pilgrimage that Allah is disassociated from the disbelievers, and [so is] His Messenger. So if you repent, that is best for you; but if you turn away – then know that you will not cause failure to Allah . And give tidings to those who disbelieve of a painful punishment.

(9:4) Excepted are those with whom you made a treaty among the polytheists and then they have not been deficient toward you in anything or supported anyone against you; so complete for them their treaty until their term [has ended]. Indeed, Allah loves the righteous [who fear Him]. 

(9:5) And when the sacred months have passed, then kill the polytheists wherever you find them and capture them and besiege them and sit in wait for them at every place of ambush. But if they should repent, establish prayer, and give zakah, let them [go] on their way. Indeed, Allah is Forgiving and Merciful. 

Now you can see that the verse has not been revealed to kill all none-believers as Christians would want you think but was directly related to those pagan Makkans who broke the treaty but God shows mearcy on them stating that if they should repent and change their evil ways then they should be left alone.

This was when the holey Prophet (pbuh) entered the city of Makkah with more than ten thousand followers. The night before the Muslims entered Makkah, the leader of Quraish Abu Sofiyan came to the Muslim camp and wanted to see the Prophet (pbuh). He confessed that his ways was wrong and he accepted Islam. The Prophet gave him an oath that no one will be harmed in his house or his court as long as they did not attack the Muslims. The huge Muslim army entered Makkah the next morning and not one person was killed or harmed. The pagans saw that the Prophet kept his word eventually all of Arabia accepted Islam due to the fairness and kindness of the Prophet who won peoples hearts.