cavalry and castles in post-roman europe

Currently in Mexico there is a movement to try to convince the United States government to give back the land that was seized in the Mexican Anmerican war. This includes New Mexico, California, and Arizonia. Now the treaty that ended the war basicaly says that this land was given to the United States in return for not sacking Mexico City. So here is the question if the United States were to give back the land do they get to sack Mexico City?

After the fall of the Romans we see a new kind of weapon on the battle feild, havy cavarly. Why is this? Was it due to the introduction of the stirrup to Europe from the Mongols, which may be nessicary for to ride a horse when covered from head to toe in metal. Or was it due to the fact that armies were a lot smaller and therefore if a couple guys were rendered invinceible due to massive amounts of armor they could do a lot more damage with fewer people.

Before and During the Roman Empire, Europe and Western Asia really did not see to many large fortifications being built. The only thing that they built that was like a castle were large walls that surrounded a town or city. After the fall of the Romans we see an expolution in castle buildings. My question is why did this occur? Was it due to the lack of money to fund building huge protective walls around entire towns and it was just cheaper to built castles. Or were castles more effective in defending towns and cities due to the fact that an army that was large enough to lay seige to the castle were quiet rare? And why is there no spell Cheack on this thing.

Hello everyone, my name is Mark Owens.  I have no idea what I am doing but I think that whatever I am doing I am doing it right.  On to the real stuf then.  I have two main questions about evolution of castles and heavy cavalry, which  will post in the next two posts.  I will also post an extra question almost everyday that hopefully try to make you think and laugh at the same time.  I hope I am doing this right.