This is a question on which an incredible amount of literature has been written during the past twenty years (thanks to various programs of excavation, notably in northern Syria and southern Israel), and we happen to have so much information that it is nearly impossible to write a synthesis. I will focus on your question on the cities, hoping that a specialist of the Monophysite world will come to help you on the other question.

• The cities were not really independant anymore in political terms, and that is a long-standing development of the Later Roman Empire. For instance, the reconstruction of Antioch after its sack by Khosrau (Chosroes) I was financed by Justinian, not by local rulers. The same can be said of the post-Justinianic era, a good example of which could be the building programme of Heraclius after his reconquest of the Levant. But they were not really administered either; actually, even if it is not really flattering for the imperial authority, they were pretty much on their own. When a hostile army came on the foot of your ramparts, the inhabitants had to organize the defense themselves (or, if they felt that their walls were not strong enough, they surrendered and paid a certain amount of money); the bishop played a very important role in that, and often acted as the leader of the citizens. Once again, the picture during Justinian's reign and after is not really different from the early 7th c.; in 611, for instance, the citizens of Apamea and Edessa yielded to the Persians; Edessa did the same thing in 544 (Antioch did not and was utterly sacked). The only thing you could really expect from the imperial regime was a tax remittance after you had been destroyed or forced to melt down everything you had to satisfy the Sassanids. So I assume that they were not really fond of the army, whose main mission was to protect strongholds, not people.

• Overall, the 6th century was a time of prosperity in the Levant; however, if you look at the Orontes Valley (Apamea and Antioch), you will get the impression of a decline. Antioch was struck by several consecutive earthquakes during the Justinianic era, and from the sack of 544, and never really recovered from all this (even though reconstruction did happen, but not on the same scale). Apamea similarly suffered from a sudden flight of its (rich — this city was characterised by the presence of very impressive houses, which suggest that it was favoured by the aristocracy) inhabitants which may have been due to the Persian invasion of 611. Afterwards, big houses were broken down into smaller entities. On the other hand, the countryside was active and rich — we still have very impressive houses in the Limestone massif not far from Apamea and Antioch, in a place which has never been occupied since (a fact which strongly suggests that even quite marginal areas in terms of productivity enjoyed a considerable wealth). And if you look at cities like Epiphania, you will see that their expansion actually takes place in the late 6th century. The Persian conquest, even if it had local consequences, did not bring important changes (for instance, we have found a mere handful of Sassanid coins in Syria; this simple fact proves that these provinces never became an integral part of the Persian Empire).

• The Ghassanid border (towns like, say, Bostra, which was the capital of Arabia, or even Rusafa/Sergiopolis) is not as well-known, but it is fair to say that the trends were similar. The area around Bostra, for instance, and Bostra itself, knew an important development, which was probably due to the trade with the Arabic world. Doubtlessly, the Ghassanids played a role in this impulse, and acted as “princes” of the area. Works like small palaces and even aqueducts were attributed to their role. As such, their revolt in the 580s is not really an attack on the region, that they were clearly beginning to transform in a territorial basis, but is rather more similar (to put it in a very simplified way) to an independance war.

• Finally, the urban life of the region was already changing. Public buildings were slowly being abandoned. It is hard to make sweeping generalisations, because it did not happen at the same pace everywhere. But there is a trend towards (1) the disappearance of important bathing complexes in favour of smaller and private baths (something we now associate with Islam, and is in fact an innovation of the Roman Levant) (2) the tentation to encroach on open areas (agoras, stoas) and (3) the disaffection of theatres. Once again, things seem to vary from one city to another; for instance, we are told that theatres fell into disuse as early as the reign of Anastasius in some places (before Justin I and Justinian), whereas someone like of John of Ephesus blames another bishop for having rehabilitated a “church of Satan” (i.e. a theatre) in Syria. Overall, it seems that the model of the ancient city was surviving as an ideology (and that the local authorities still prevented, for instance, people from building shops on the streets), but that its social functions had disappeared.

I am only scratching the surface of a fascinating place in a fascinating time. Articles by Clive Foss would provide you with an expanded version of my answer, with more details, more plans, more pictures, and better English (esp. Syria in Transition, AD 550-750). You should also try to find Hugh Kennedy's article From Polis to Madina, a classic. Then on the religious aspects that I have not covered in my answer, it is harder to provide a bibliography because I do not see any seminal article on the topic. General handbooks often offer interesting synthesis on this subject. Justinian and the Making of the Syrian Orthodox Church is quite specific but makes interesting points. Otherwise, you might have a look at Herrin's Formation of Christiendom, a great synthesis.

/u/georgiusflorentius covers the subject magnificently until just before the Persian/Arab wars. However, it would be very safe to say that everything changed afterwards.

Over the course of the 7th century, almost all the cities of eastern regions that weren't immediately captured and held by the Arabs (like say Antioch) were completely decimated through the decades of raiding on the hinterlands of the various cities. John Haldon has a terrifying list of the frequency and the repeat of the siege and capture of cities in the whole of the region, with one city Amorium being besieged and captured an astonishing 8 times before finally being sacked and razed to the ground in the 9th century. Many cities were put to siege and taken at least once, with multiple recaptures being not uncommon for cities as far away from the border as Smyrna and Nicaea.

Needless to say, this had a massive effect on the economy and survival of these cities, as without the stability of the countryside for farming and trade, the cities themselves were frequently abandoned, or if surviving, left only as military strongholds a fraction of the size and population of the old city which had existed since antiquity.

As for the Melkites, it seems that they were mostly left alone in the parts of eastern regions that were under the authority of the Arabs, but as for the rest of the Byzantine Empire, the shock of such a dramatic loss in territory caused the entire societal identity to fold sharply into the structures of official orthodoxy and the state bureaucracy. It became an essential element of Byzantine survival, and theological changes were only made when backed by military success (which is one of the may explanations for the rise of iconoclasm).

This was sadly the case for the two centuries after the Arab conquest until the Macedonian Dynasty. There were few if any "cities" except Constantinople, and maybe Thessalonika. An Arab chronicler is recorded as saying there were only 5 "real" cities throughout the whole of the remaining Roman (Byzantine) Empire left. Compare this to the multitude that existed in antiquity. The population was definitely still agricultural, but the security situation meant many people who were previously farmers, switched to pastoral herding to make a living. There were definitely a lot of priests, and within Constantinople the occupations would reflect the massive increase in the state bureaucracy, and the supporting trades for that bureaucracy.

And with that said, the state was all encompassing at the time. There was almost no political autonomy for the outlying regions, everything had to be done through the politics of the capital city because there really weren't any other cities or even power centers. For a long time in fact, it didn't matter if a large portion of the eastern armies decided to rebel. So long as they didn't control the capital, such a revolt would quickly fizzle out as the pay, the infrastructure, and the culture was all based out of Constantinople.

However, that is as specific as we can detail. There are almost no records surviving from the time of Byzantium in its peak crisis years of the mid 7th to early 8th century. Almost everything we know was written in 9th century chronicles looking backward, with the 9th century being the decade that the Byzantine Empire started restabilizing and going on the aggressive counterattack.

Once you get into the 9th century, cities start reviving, trade starts coming back, as well as aristocrats and military independence. And from that point on, I'm going to have to stop as the world of Macedonian Dynasty Byzantium can be seen as different from crisis era Byzantium as that era is from Justinian's era.

Hopefully we can have someone else drop in to fill that final gap for you, if you're interested.