I don’t know if I can answer every part of this - there are a lot of questions in here! I should leave the military stuff for another historian. But I can start off with what life was like in Jerusalem and the surrounding area when the First Crusade arrived.

First of all, the people living there were very ethnically and religiously diverse. There were native eastern Christians, including Greek Orthodox, Armenian, Coptic, Nestorian, Georgian, Ethiopian, Syriac, and Maronite Christians. There were also Jews, including the Karaite sect, and a small number of Samaritans.

The Muslim population was divided into Sunnis, whose spiritual head was the Abbasid caliph in Baghdad, and Shi’i. At the time, the Abbasid caliph was mostly just a figurehead, and political power was held by the Seljuk sultan. The Seljuks were nomadic Turks from Central Asia and their sultan ruled in Baghdad, but several other Seljuk emirs and atabegs ruled the cities of Syria somewhat independently.

By 1099, Jerusalem was controlled by the Shi’i Fatimids, who had ruled Egypt since 969. The Sejuks had captured it in 1070, but the Fatimids took it back in 1098 while the Seljuks were distracted by the crusade, then of course the Fatimids lost it to the crusaders in 1099. There were also offshoots of the Shi’i, such as the Druze in the mountains of Lebanon, and the Nizaris, who established an independent state in Syria in 1094. The Nizaris would later be known to the crusaders as the famous “Assassins.”

We don’t really know exactly how many people lived in Jerusalem, or the territory of the future crusader states, but Josiah Russell calculates that all of Syria had about 2.3 million people at the time of the crusades, living in perhaps eleven thousand villages. The crusader Kingdom of Jerusalem may have had as many as three hundred and sixty thousand people, including two hundred and fifty thousand rural villagers.

According to the Persian traveller Naser-e Khosraw, who visited around 1050, the population of Jerusalem was about twenty thousand people, and the city was always full of Christian, Muslim, and Jewish pilgrims. Ibn al-Arabi, who visited Jerusalem only a few years before the crusaders arrived, mentions Sunnis living in Jerusalem, but says the cities along the coast and elsewhere in Fatimid Palestine were majority Shi’i. Christians and Muslims had lived together in Jerusalem until 1063, when they were segregated into separate quarters. The Christian community controlled the Church of the Holy Sepulchre, and, outside the city, the town of Bethlehem. The Holy Sepulchre had been destroyed by the Fatimids in 1009, but was rebuilt starting in the 1050s (and then the crusaders later modified it into its current structure in the 1150s)

Under the Muslims, Christians and Jews were dhimmis and paid a specific tax, the jizya. That didn't really change when the crusaders arrived; they basically adopted that system, but the Muslims had to pay the jizya to the crusaders. The cities were sometimes governed by a qadi (an Islamic judge) or a ra’is (Arabic for “head” or “mayor”), or more directly by a Seljuk or Fatimid governor. In rural areas there was also a semi-feudal system that the crusaders found familiar and easy to adopt: land was granted as an iqta and revenue was collected by the muqta, who could rule the iqta as an independent fief.

So, that was the situation that the crusaders found when they arrived in 1099.

The capture of Jerusalem on July 15, 1099, was gruesome. According to Fulcher of Chartres, “if you had been there your feet would have been stained to the ankles in the blood of the slain…None of them were left alive. Neither women nor children were spared.” (chapter 1.27.13, pg. 122)

There's some debate about whether the massacre was as enormous as reported in the chronicles; it may be a literary invention based on Biblical descriptions of similar massacres, but in any case, it’s probably true that the crusaders killed most of the defenders, whatever their number. Jerusalem may have been packed with refugees fleeing the crusaders while they were moving south, but it’s also possible that the Fatimid governor had expelled all of the eastern Christians, at least (fearing that they might defect to the crusader side). So we don’t really know who was left there to defend it in July 1099. But we do know a bit about the nationalities of the crusaders: Fulcher lists French, Flemings, Frisians, Swiss, Germans, English, Scots, Italians, and Bretons, among probably many others.

There have been some previous questions about what both sides thought about each other. Basically...they didn’t know anything about each other at all. The crusaders dd not know or care what Islam was. They eventually realized that there was a difference between Turks and Arabs, and that the Fatimids believed in a different kind of Islam. The Muslim side mostly had no idea where the crusaders were from (they often assumed it was just another army from the Byzantine Empire), or why they wanted Jerusalem.

I’ll link to the earlier questions rather than repeating everything here:

I'm a Crusader heading towards the Holy Land in 1096. How much do I understand about Islam?

During the First Crusade, what opinion did the Turks and Arabs have of the Franks / Crusaders?

What stereotypes or preconceptions did the Arab world hold about Europeans during the Medieval era?

Hopefully that answers some of your questions!

Sources:

- Joshua Prawer, “Social classes in the Crusader States: The ‘Minorities’” and Josiah C. Russell, “Population of the Crusader States,” both in Kenneth M. Setton, ed., A History of the Crusades, vol. V: The Impact of the Crusades on the Near East, ed. Norman P. Zacour and Harry W. Hazard (University of Wisconsin Press, 1985)

- Ronnie Ellenblum, Frankish Rural Settlement in the Latin Kingdom of Jerusalem (Cambridge University Press, 1998)

- P.M. Holt, The Age of the Crusades: The Near East from the Eleventh Century to 1517 (Longman, 1986)

- Carole Hillenbrand, The Crusades: Islamic Perspectives (Edinburgh University Press, 1999)

- Benjamin Z. Kedar, “Some new sources on Palestinian Muslims before and during the Crusades”, in H.E. Mayer, ed., Die Kreuzfahrerstaaten als multikulturelle Gesellschaft (Munich, 1997)

- Benjamin Z. Kedar, “The subjected Muslims of the Frankish Levant,” in The Crusades: The Essential Readings, ed. Thomas Madden (Blackwell, 2002)

- Benjamin Z. Kedar, "The Jerusalem Massacre of July 1099 in the Western Historiography of the Crusades." Crusades, vol. 3 (2004)

Primary sources:

- William of Tyre, A History of Deeds Done Beyond the Sea, trans. Emily Atwater Babcock and A.C. Krey (Columbia University Press, 1943)

- Fulcher of Chartres, A History of the Expedition to Jerusalem, 1095-1127, trans. Frances Rita Ryan, ed. Harold S. Fink (University of Tennessee Press, 1969)

- Naser-e Khosraw’s Book of Travels, trans. W.M. Thackston (Bibliotheca Persica, 1986)