As I understand it, earlier during the Merovingian period, they attempted to copy many aspects of Roman technology. Did this extend to weapons as well?

So, I'm not quite sure what you mean by copying many aspects of Roman technology? The Franks certainly copied Roman style rhetoric in their writing, but if you're talking about high imperial era engineering or military technology, no the Franks weren't busy rebuilding bath hypocasts or refashioning lorica segmenta to wear out in battle.

The limited data we have on weaponry and armor for this era shows for the horsemen to be a general continuation of late Roman armor, chainmail (for those who could afford it), round shields, javelins/spears, and slightly less often swords.

Although as a note, I'm not sure "advancement" would be the right word for what was happening with weapon technology. "Adaptation" might be better choice. The Franks adapted to fighting in a world completely different from that of the Romans with their tax-paid forces, their defensive limes, and their logistically supplied field armies.

if you could even simply give rough estimates as to how many people lived in towns versus villages, it'd be very helpful. Also, how was wealth distributed between the two? Did the wealth tend to concentrate around the rural areas

At the peak of the Roman Empire, the urban population was estimated about 10-20% of the population, with Egypt being the outstanding exception at 33%. Though southern Gaul had more cities than northern Gaul, a lot of the archaeology of cities in the post-Roman period show a far lower, almost barely detectable level of settlement.

Considering too, that the majority of the power centers in Frankish Gaul were actually in the rural countryside, as opposed to Italy where the elites were focused in the cities, and an estimated 50% decline from peak Roman population of Europe during the Early Medieval era I would definitely wager a guess of around 5-10% of the Frankish population living in the cities. Especially after 640 CE with the breaking of Mediterranean trade by the Arab conquests.

As for the wealth concentration, I definitely feel more of it was focused in the rural areas. Wealth in the early medieval world (and ESPECIALLY Francia) was all about land, ownership of it, control of offices with jurisdiction over it, and so on. Though counts could reside in cities, their power wasn't in the city itself. It was in the control of the land around the city.

Though urban churches could be rich as well, they too were predominantly rich in land. As previously mentioned, the archaeology done so far of Frankish cities tend to show a poverty of material wealth. There is of course, the possibility it's only because we haven't developed better ideas as to how to spot social wealth in this era, but all we can say now is the evidence that we have now using the knowledge we have now doesn't show it being there.

Not to mention that what we think of as cities may merely be our poor translation of "civitates", which could just mean their jurisdictional area based around the former city. Sorta like an official living in a township as opposed to a town.

Were permanent, or semi-permanent fortifications erected? Or were they far more mobile than that?

I believe some of the AHers here are in fact studying archaeologically some of the Saxon frontier fortifications put up during the Carolingian era as they were trying to expand eastward. So yes there were semi-permanent fortifications, but obviously a Frankish army was well adept at setting up mobile camps, like the siege camps of Charlemagne outside Pavia when he invaded Italy.

Sources:

• Wickham, Chris. Framing the Early Middle Ages: Europe and the Mediterranean 400-800. Oxford: Oxford UP, 2005.

• Nicolle, David. The Age of Charlemagne: Warfare in Western Europe 750-1000 AD. London: Osprey, 1984.

• Gregory. The History of the Franks. Harmondsworth: Penguin, 1974.

• Bachrach, Bernard S. "Charlemagne's Cavalry: Myth and Reality." Military Affairs, Vol. 47, No. 4 (Dec., 1983), pp. 181-187