One of the main reasons for the relative decline of ancient Egypt was the lack of wood to make charcoal. While bronze can be rather easily melted and then cast into the shapes needed and is very hard from the outset of being made, iron requires more long-time work (beating out impurities, heating with carbon and so on) to be made into wrought iron with steel-like properties. Unworked iron is actually softer than bronze.

Traditionally, the Egyptians took their wood from the cedar forests of Lebanon, or from the Levant in general, but towards the 10th century BCE this area was dominated by the Assyrian Empire and despite many attempts the Egyptians never were strong enough to return. Since Egypt lacked this source of fuel, it had a hard time reacting to the exhaustion of the tin sources of the Eastern Mediterrenean and the switch from bronze to iron, and Egypt was conquered many times. Proto-berber tribes conquered northern Egypt and while their power eroded, Egypt was then conquered from the south by Nubians.

Egypt was then ruled by Nubians, before being invaded by the Assyrians. It was then fought over between Nubians and Assyrians until it briefly regained independence, fought the Babylonians and was then crushed by the Perisans. It remained a part of the Persian Empire until Alexander the Great conquered it. After his death the Ptolemaic dynasty ruled the land in a Greek fashion until the country was integrated into the Roman Empire at the death of Cleopatra VII Philopator (the famous Cleopatra of history, yes, she was Greek-Macedonian, not Egyptian, even though the Ptolemaic dynasty had adopted some of the old customs of Egypt).

Egypt became christian when the Roman Empire adopted christianity as its state religion.

By the time the Arabs invaded, the Roman Empire had been at war with the Persian Empire for two decades and was severely weakened. Egypt was also embroiled in a bitter struggle over faith, and many of the persecuted side greeted the Arabs as liberators.

I can add to /u/vonadler 's point by touching on the second part of your question about Egypt's conversion to Islam, although I will disagree a bit with his last sentence.

The ability of the Roman Empire (by this point in the early 7th century we're dealing with the Byzantine Romans) to resist the Arab conquests in the Levant and most of North Africa was basically dashed by their total defeat at the Battle of Yarmouk.

As /u/vonadler said, the Romans had been fighting the Persians for decades before this, and although the Byzantine Emperor Heraclius was on the verge of a total victory against the Persians, the campaign had basically exhausted the Byzantines militarily. After his army was defeated at Yarmouk there was no hope of any kind of relief expedition for any of the interior garrisons that were swiftly taken by the Arabs in the conquests.

This included Egypt, although Alexandria was a bit of a tough nut to crack given that it was able to be reinforced and resupplied by sea. But the entirety of Egypt was firmly under Arab control by the end of the 7th century.

Where I disagree with /u/vonadler, at least in the context of your question, is about the views of Egypt's residents towards the Arab conquerors. While it has been suggested that Egypt's Christians, predominantly Monophysite Copts who had serious disputes with the imperial church, might have "welcomed" the comparative religious tolerance of the Arab invaders, I think the general consensus among historians is that this this has been a bit overstated. If you read the contemporary accounts you certainly don't get the impression that the Arabs were "welcomed as liberators."

edit: to quote Robert Hoyland on this matter: "Modern scholars often argue, on the basis of later witnesses, that the Egyptians who were anti-Chalcedonian [e.g. Copts]...welcomed the Arabs and only the Chalcedonian Egyptians opposed them. However, John of Nikiu [a key contemporary Egyptian chronicler] never once intimates that he or his fellow anti-Chalcedonians were in any well well disposed toward the conquerors. He also makes clear that the Arabs themselves were indiscriminate in their slaughter and that the disunity among the Egyptians lay not in sectarian differences but in how to face this challenge: whether it was better to submit and make peace or to stand and fight." NB here, however, that the "indiscriminate slaughter" was largely reserved for those communities that stood and fought and the Christians of Egypt did, eventually, secure quite reasoanble terms of peace.

Also in the context of your question if they did feel liberation it was, of course, to better practice their form of Christianity.

As for their conversion to Islam, that has much to do with changes in both Islam itself as well as in the particular way in which the Arab conquerors administered their territories.

Initial conversion to Islam was slow not just because of the newness of the religion but because, initially, in order to convert to Islam you also had to join yourself to an Arab tribe. Islam as a truly universal religion for Arab and non-Arab alike and in which conversion was encouraged was a later development. Some of the first evidence we have for such a policy are the inscriptions in the Dome of the Rock, built in the reign of the Ummayad Caliph Abd Al Malik (r. 685-705.)

Converts to Islam converted for any number of reasons. For one thing, and particularly in the early period, conversion brought economic benefits as Muslims did not have to pay the poll tax imposed on non-Muslims (the extent of this benefit would decrease later on when Muslims, too, started to join the tax structure of the new empire).

Then of course there were genuine believers among the converts. Islam makes a number of arguments to the effect that it is the perfect completion of the Abrahamic faiths and from the time of Abd Al Malik onward those arguments became a policy of state.

The Arab Muslims also intermarried with the local community, as well as settling large portions of their troops in Egypt. The Roman settlement in the area of Modern Cairo (called Babylon) was a relatively minor settlement until the Arabs settled in nearby Fustat.

The elites of the administrative state also Islamized over time as well, so while the administration of Egypt was initially bilingual Greek and Arabic with most of the bureaucracy simply retaining their positions from the ancien regime, once again Abd Al Malik seems to have been critical in Arabizing and Islamizing the administration of the provinces so that within a couple hundred years conversion was connected to advancement.

With all of these pull factors, and despite the general comparitive tolerance of Islam and the Arabs for Christians and Jews, there were also "push factor" policies put in place, albeit unevenly. Among the most famous of these is that Christians could be, at various times and again, unevenly, prevented from building new Churches or restoring old ones. Another noticeable change following the conquests would have been that, in general, the ringing of church bells would have been banned and, instead, the sound of the Islamic muezzin's call to prayer would have become the dominant sound of religion in the public square. There were also, on occasion, more straightforward examples of persecutions and religious violence towards Christians and Jews over the centuries.

Nonetheless, in comparison with the former Persian territories for example, where some 95% of the population had converted within two centuries of the conquests, conversion in Egypt was much slower and much less complete. Down to the present day some 10% of the population of Egypt remains Coptic Christian and those numbers have basically been stable for centuries. Also until the 1940s and the foundation of Israel, Egypt had a substantial Jewish community as well.

There are a number of reasons for this, and as far as I'm aware no conclusive consensus about why the Copts held out. Important factors, in contrast with the situation in Persia, include a better defined Church hierarchy which had been culturally elite under the Byzantines. In Persia, while Nestorian Christians were the majority, they had been ruled by a Zoroastrian elite. The Copts also occupied a unique ethno-linguistic position with the Coptic-Egyptian liturgical language. The Egyptian territories, while unified, also underwent a greater number and degree of rulership changes than Persian/Mesopotamian core of the Islamic empire, so that for the first two hundred years Egypt is ruled by orthodoxic Muslim rulers until 909 when the Shia Fatimids take over (I hesitate to describe Orthodoxy as "Sunni" in the early years, but that's a separate discussion). Followed by the Sunni Ayyubids and then the Mamluks.

Although its estimated that the majority of Egypt was already Muslim by this time, its under the Mamluks (1250-1517) that Egypt's conversion is finally pressed home, largely as the result of more concrete policy oriented versions of all the factors I mentioned earlier.

It's also worth noting how family law in Egypt operates, which follows the Sharia and impacts on why the Christian population of Egypt is still stable today (Obviously I don't want to get into 20 year rule territory, but these laws have been on the books for some time, Sadat enshrined the Sharia basis article in the Egyptian constitution in 1980.) The child of a Muslim man, is, by law also a Muslim. Marriage of a non-Muslim woman to a Muslim man is legal, while marriage of Muslim women to non-Muslim men is illegal. Conversion to Islam is allowed, while conversion from Islam is illegal as apostasy. The result is that there is intense social pressure against interfaith communal and familial mixing, which has contributed to keeping that 10% Christian minority rate stable.

Source wise:

In God's Path by Robert Hoyland is an excellent single volume history of the conquest period and early Arab rule and includes accounts of what the Egyptians thought of their new rulers.

Richard Bulliett's Conversion to Islam in the Medieval Period is the standard quantitative look at when, where, why and how people converted to Islam in this period, broken down by region, it's also quite short which is nice, although his sources for Persia are much better than those in other territories.

For policy towards Christians in the Mamluk period, see, for example, the article Coptic Conversion under the Mamluks by Donald P. Little.

For the outlook of the early Islamic state, particularly its organization and the creation of Muslim polity see the two articles The Formation of the Islamic State by Fred Donner and New Documentary Texts and the Early Islamic State by Robert Hoyland.