North Africa at this time was part of the Eastern Roman Empire and it was a region known for its wealth - Egypt was the breadbasket of the empire, as it fed Constantinople and had a highly commercialised economy, and although the area around Tunisia was no longer as rich as it was during the high imperial period, it was still a prosperous region. I don't know much about what is now modern-day Libya, Algeria and Morocco, since as far as I know we don't have any literary sources talking about these provinces in any detail. As for religion, due to its long history within the empire, Christianity was well-entrenched throughout the region, though I'm sure that some pagans still existed even by the seventh century.

Strictly speaking, North Africa does not refer to Egypt when the term is used by Byzantinists, but I'll talk about the conquest of Egypt as well just in case you meant to include it. As I said, Egypt was fabulously wealthy, but in the 610s the Eastern Roman Empire was embroiled in a catastrophic war with the Persians, which led to the occupation of the Roman Near East until 628. Between 608 and 610, Egypt was also the scene of a Roman civil war, as partisans of the usurper Heraclius fought to dislodge the forces of Emperor Phocas (who was another usurper); Heraclius won in the end, but he was definitely not an emperor everyone supported. There were also tensions within Egypt, since the majority of the population were Miaphysite Christians, whilst the Constantinopolitan regime was firmly Chalcedonian, not to mention the huge wealth gap between peasant tenants and aristocratic landowners. Religious divisions escalated in the 630s when Roman rule returned to the region, as Heraclius imposed a new religious doctrine, Monoenergism/Monotheletism, on his empire. Depending on how your interpret the sources, the Miaphysite Church either compromised with the government or was bitterly persecuted, but either way, it made a lot of people very angry.

As for the conquest itself, our best source is John of Nikiu, a Miaphysite monastic administrator who wrote a universal chronicle that ended with the Arab Conquest of Egypt a generation afterwards. He was clearly quite knowledgeable about recent Egyptian history and his material is generally more trusted than later, more extensive Islamic accounts (which were compiled from oral accounts only in the mid-eighth century). The problem is that his chronicle is confusingly organised and its English translation unbelievably shoddy (you can read it for yourself here), which may have misled past historians about the events he wrote about. This is a particularly annoying problem as A. J. Butler's book on the conquest of Egypt, published more than a century ago, is still the most extensive account of this campaign.

Instead, I'll base my answer on the recent but less fleshed out accounts of P. Booth and J. Howard-Johnston. Both historians suggested that the conquest occurred in a round-about fashion. In Booth's telling (which can be found here), there were multiple Muslim armies when Amr invaded n 639 and that one army followed the coast south and then attacked from the Upper Nile, effectively attacking from behind Roman defences, whilst Howard-Johnston suggested (in his Witnesses to a World Crisis) that Amr launched an attack on Oxyrhynchus and cut Egypt in two. In either case, Amr was an astonishingly good general and he should be praised for his generalship. The Romans definitely did not go down easily though, since fortresses like Babylon (in modern-day Cairo) was not taken by force and Romans armies regrouped again and again after being defeated. A truce was made under Cyrus, the Chalcedonian Patriarch of Alexandria/effective governor of the province, to evacuate Roman forces from threatened areas, but Heraclius wanted his armies to fight rather than to peacefully hand-over Egypt, so Cyrus was removed. Heraclius died in 641 and his successors abjectly failed to defend their eastern possessions because of infighting between his sons Constantine III and Heraklonas. The former died within months, but court intrigue quickly removed Heraklonas and placed Constantine III's son, Constans II, on the throne. Constans was only 11 in 641 and his regency government oversaw the Romans' final defeat in Egypt. An expedition was sent to 645/6 to take Egypt back, but only Alexandria was occupied and within months they were defeated again.

This isn't to say that all the Romans put up a good fight, since I don't see why Miaphysite Christians would fight particularly hard against an invading army that did not plan to persecute their brand of Christianity, whereas the central Roman government had done so for more than a century. More generally, there was little point for anyone to fight to the death, since Egypt was occupied two decades ago under the Persians and the same things had happened then too: after a few major military defeats, cities were content to surrender and make a deal with the invaders. Regardless of why the province fell, we do know that many Roman officials, even governors, continued to serve the new Arab regime. Personally, I'm inclined to think that that the Miaphysite Church was even quite happy to be ruled by Arabs, as John of Nikiu, the source I mentioned above, went out of his way to criticise Roman apostates and corrupt governors, but was exceedingly fair to Amr, the man who had conquered Egypt.

As for conquests further west, the evidence is more fragmentary, as unlike Egypt, Armenia, and Syria, we have no contemporary sources for the region's conquest, but even so in Islamic sources it is clear that the conquest was gradual and piecemeal. Here, I will primarily use the work of R. Hoyland (In God's Path) and W. Kaegi (Muslim Expansion and Byzantine Collapse in North Africa), both of whom wrote about this within the last few years. The first attack on Tunisia was around 647/8, possibly as a reprisal for the Byzantine expedition that had retaken Alexandria in 645 or 646. At this point Byzantine North Africa was actually in revolt against Constantinople, as the local governor, the Exarch Gregory (who was also most likely related to the imperial house), had rebelled against Constans II for religious reasons - he was a Chalcedonian Christian, whilst Constans had continued his grandfather's policy of favouring Monotheletism. Conveniently for Constans, Arab raiders ended up defeating Gregory, who had gathered an army to fight them. After the defeat of Gregory, there is no indication that the Arabs made any permanent gains and Muslim sources stated that local Romans asked ‘Abdallah ibn Sa‘d to take tribute from them and then leave the country. He accepted and returned to Egypt "without appointing anyone over them or establishing any garrison there".

Then there was a period of calm, possibly due to the first Arab civil war (656–661), before the victorious Caliph Mu'awiya launched a general offensive on all fronts in the 660s, with a major invasion of Africa attested to in 670 and of course the founding of Qayrawan, their new base of operations. There was another lull as the Arabs and Roman fought elsewhere in the Mediterranean, possibly because with Constans II's death in 668 in Sicily there was no longer a threat from the Roman navy in the west, so Arab military forces can be shifted to the more important east. The lull continued into the second Arab civil war (682-692), with a papal source suggesting that Roman control was completely restored around 685/6. A second major push into Africa began under the Marwanid Caliphs from the 690s onwards, which finally ousted the Romans from North Africa.

As you can see, the conquest of North Africa was anything but easy, since it took roughly six decades for the Arabs to assert their control throughout the region. Roman forces seemingly had naval superiority throughout this period and wealthy coastal cities like Alexandria and Carthage did not fall to military force, but were abandoned for strategic reasons. Admittedly, outside of Egypt centralised control was limited to only the cities, so the many Moorish tribes that populated North Africa were only ruled loosely by the Romans. Still, despite their fierce independence they were generally Christians and the Moors who resisted the Arabs throughout the seventh century should be seen as Roman loyalists rather than tribes acting independently.

I'm not very familiar with the languages North Africans spoke, aside from the fact that Egyptians would have spoken Coptic, and that government officials in Egypt would have used Greek as well. For the rest of North Africa, Latin would have been favoured by the elite for bureaucratic purposes, though I'm sure a great many would have known Greek too, I unfortunately do not know which language the less well-off city-dwellers or the Moors spoke. I also can't say much about how accepted Islam was, aside from the general comment that as Arabisation took centuries to occur, people did maintain their Christian identity for a very long time; as I said, Islam was not a religion that was out to get Christianity. I believe that that the Moors converted in large numbers quite quickly though, so this issue is clearly a lot more complicated than my summary. Hopefully someone else here will help you to fill in the gaps! My comments on why the Arab Conquests were successful and Christian responses to it may also be relevant :)