There is one significant thing I can think of when it comes to the Empire and Christianity. When Constantine took over and started letting Christianity in, the one thing he did was get rid of the hole Roman legal system which was completely corrupt to the Christians which actually, at the time, was far better. It might be worth a thesis to find out more about this in some way, but by this time the Empire was on its last legs as it was known before.
I think the whole idea that Christianity was the cause of the fall of the Roman Empire may be little overblown. It had a factor to be sure, but there does seem to be a new movement out there pointing to other factors such as slavery, the Empire being to dependent on foreign mercenaries rather than their legions for defence, the legions themselve being diminished in quality, etc. I think the fact that the Romans seemed to shift in their mentality from building an Empire to just enjoying their empire without considering external threats seems to be the largest factor to me.
Empires by their nature make to many enemies from without and within -- The fact is that the Empire was built on the ashes of the Republic, which did more to build Rome than the Empire. I don't think some forgot that.
I don't know about that, I think greed and desire for power has more to do with wars than religion. Religion often gets used by the power hungry to justify their cause, but the real motive for wars seems to be more along the lines of I want this peace of land these people's money. It goes something like this -- "I want to invade Egypt because I want to control the grain supply and make a fat profit, because I want to be the middle man -- Hmmmm. Which preist of Mars can I get to justify this religiously" Sorry the root cause of wars seems to be more the desire to have something that somebody else has than religion.