There were some really good questions during our discussion time and I wanted to offer some (hopefully) succinct answers to a few questions I imagine are very common from these passages.
Q: Why so many plagues and why so severe? Was God just wielding the ten plagues like a playground bully, twisting Pharaoh's arm until he cried "uncle"?
A: No, it was much more than just a battle of the wills. Egypt was a pantheistic society, which means they worshiped many gods. Each of the ten plagues was direct challenge (and defeat) of one or more of those gods in the minds of the Egyptians. In essence, God was demonstrating his superiority and sovereignty over all of the created order and the supposed corresponding Egyptian pantheon. Pharaoh and all the Egyptians would have rightly understood this as a sort of clash of the titans, with the Israelite God emerging as the clear victor.
For instance, darkness was an assault on the sun god, Ra. The Nile turning to blood was an attack on Hapi, god of the Nile. With each plague, the Israelite God worked his way up the rungs of the Egyptian pantheon, finally reaching the Supreme: Pharaoh himself. The Egyptian religious system held that the Pharaoh was a human incarnation of Ra and that he was a god-king. So the death of Pharaoh's first born was the death of the son of god, the god-in-waiting.
Not only was this final plague seen as the defeat of Egypt's preeminent god figure, but within it (and the Passover sacrifice and meal) was a beautiful foreshadowing of both the Old Testament sacrificial system and the eventual perfect sacrifice of Jesus Christ, the Lamb of God. So in each of the plagues—but especially the last—God is anything but a mere bully and arbitrary in his actions.
Q: Were all the other Egyptians (and the Israelites, too) just innocent victims suffering collateral damage in this battle of the gods?
A: No. God demonstrated his ability to execute a surgical strike when necessary. The land of Goshen, the Israelite district within Egypt, was spared some of the plagues like those of flies, darkness and livestock. We are even told that some Egyptians were spared the worst of certain plagues when they "feared the word of the Lord" and responded properly (see the account of the hail for example).
However, it is conceivable that God had designs even for those plagues that afflicted both Egyptians and Israelites indiscriminately. After all, even the Israelites delayed in honoring, fearing and obeying the direction and word of the Lord through Moses.
It is also reasonable to assume that Pharaoh was not the only Egyptian holding out hope that one of the higher and mightier deities might finally put an end to this God of the slaves. In fact, there is never any account of any repentance or pleading for mercy or sanctuary on the side of the Egyptian people. This idea seems supported by the fact that there is no account of any Egyptians fleeing to Goshen during some of the more localized plagues. Whether they still held out greater hope in their gods (and Pharaoh) or whether they simply feared Pharaoh more than God, the silence of the Egyptian population doesn't necessitate their innocence.
Q: How do we make sense of the biblical account when it says "God hardened Pharaoh's heart"?
A: This is probably one of the most common and challenging questions from the entire book. One question that I have found important to ask about this problem is: "What action is required of God in order for Pharaoh's heart to harden?"
The Bible does declare emphatically that "God cannot be tempted by evil, nor does he tempt anyone; but each one is tempted when, by his own evil desire, he is dragged away and enticed." (James 1:13,14) So God would not tempt Pharaoh and in deed did not need to if Pharaoh's own evil desire and inclination was already against God. If this is true, than all that would be required is for God to release Pharaoh and turn him over to his fallen tendency towards hardness of heart. This same progression of fallenness is shown in Romans 1 when Paul writes three times that God "gave them over" to sinful desires, shameful lusts and a depraved mind. So while God may be the passive agent releasing fallen mankind to do whatever they desire, Pharaoh and the rest of humanity would be the active agents in our sin and rebellion. Our fallenness simply dictates what we do with our freedom when God turns us loose.
The biblical writer of Exodus communicates as much when switches back and forth between the idea the God hardened Pharaoh's heart and Pharaoh hardened his own heart (Ex. 8:15, 32). Certainly the author was not implicating God in Pharaoh's sinfulness, but it does seem he sees even Pharaoh's willful, sinful hardness as under the sovereign allowance of God.
In summary, the Bible always keeps these two ideas in balance and tension: the active willful rebellion of mankind within our freedom and the passive allowance of that rebellion under the sovereign rule of God. In this way, both the moral responsibility of man and the ultimate sovereignty of God is preserved.