However, it is stated openly by many Muslims that the world is divided into the House of Islam, which are areas ruled by Islamic law and the House of War, which are areas not ruled by Islamic law. These countries will be offered the possibility to accept Islam and, if they do not, Muslims will be justified (or are they obliged to, that's the part I am not sure about) to invade them and subject them to Islamic law. Is this a correct understanding of this House of Islam/House of War dichotomy?
Muslims did not just take over countries to rule over them as kings and rip their resources, the status quo was that whoever gained enough power just ennexed other lands to their kingdom and demanded a permanent tax - regardless of who they were.
the Muslim rulers would send epistles to the kings of other lands
1. inviting them to Islam
2. giving them the option to pay the tax to them instead of it stopping at the current occupying king - whether from Rome or Persia or anywhere else - and allowing them to tell people about Islam.
3. war
if they accepted the first two the Muslim Caliphate would be duty bound to protect them from any external threat.
anyone who accepted Islam was no longer required to pay (proving that they didn't have their own "lordship" and financial gain in mind).
anyone who was weak or poor or unable to pay was exempt and would even receive benefits
History has recorded many examples of Muslims fulfilling their sacred promise towards the dhimmis. The companion of Prophet Muhammad, Abu Ubayda al-Jarrah, was the leader of the army that conquered Syria. He made agreement with its people to pay the jizya.Realizing the faithful loyalty of the Muslims, the Syrian people of the covenant resisted Muslim enemies and aided the Muslims against them. The residents of each town would send some of their people to spy against the Byzantines, who conveyed the news of the gathering of Byzantine army to Abu Ubayda’s commanders. Finally, when the Muslims feared they would not be able to guarantee their protectect ,Abu Ubayda wrote to his commanders to return all the money they had collected as jizya with the following message for the Syrians:‘We are returning your money to you because news has reached us of the awaiting armies. The condition of our agreement is that we protect you, and we are unable to do so, therefore, we are returning what we have taken from you. If God grants us victory, we will stand by out agreement.’When his commanders returned the money and conveyed his message, the Syrian response was:‘May God bring you back safely to us. May He grant you victory. If the Byzantines had been in your place, they would not have returned anything, they would have taken everything we own and left us with nothing.’The Muslims were victorious in the battle. When people of other towns saw how their allies were defeated, they sought to negotiate a truce with the Muslims. Abu Ubayda entered into a truce with all of them with all the rights he had extended in the first treaties. They also requested that the Byzantines hiding among them be given safe passage back home, with their families and possessions, without any harm, which Abu Ubayda agreed to.Then the Syrians sent the jizya and opened their cities to welcome Muslims. On the way back home, Abu Ubayda was met by the representatives of townspeople and villagers requesting him to extend the treaty to them as well, to which he happily complied.
Umar ibn al-Khattab the second caliph of Islam, once passed by a old, blind man begging in front of a house. Umar asked him which religious community he belonged to. The man said he was Jewish. Umar then asked him, ‘What has brought you to this?’ The old man said, ‘Do not ask me; ask …poverty, and old age.’ Umar took the man to his own home, helped him from his personal money, and then ordered the head of the treasury, ‘You must look after this man and others like him. We have not treated him fairly. He should not have spent the best years of his life among us to find misery in his old age.’ Umar also relieved him and others in his situation of paying the jizya.Another example is found in Khalid ibn al-Walid’s letter to the people of the Iraqi city of Hira. It contains the terms of truce he offered them:‘If God gives us victory, the people of the covenant will be protected. They have rights promised to them by God. It is the strictest covenant God has made incumbent on any of His prophets. They are also held by the duties that it places upon them and must not violate it. If they are conquered, they will live comfortably with everything due to them. I am commanded to exempt from jizya the elderly who cannot work, the disabled, or the poor who receive charity from their own community. The treasury will provide for them and their dependants as long as they live in Muslim lands or in the communities of Muslim emigrants. If they move outside of Muslim lands, neither they nor their dependants shall be entitled to any benefits.’
so you see it was not as simplistic as the orientalists would have you see it