Can someone describe the power structure of the feudal system and the relationship between lords and serfs?

Answer 1

I think you mean "lords and vassals." Lords were the noblemen and kings while Vassals were the peasants ad serfs. Lords protected the Vassals in excahge for food/labor.

A basis where those with armies would protect/defend the farmers. But in exchange for that protection the farmers had to take an oath of fealty and feed/work for their lord (guy with the army), the farmers became vassals to the lords and were later called "peasants" or "serfs"

That is the basis, although in many cases the lords abused their vassals, a majority managed to survive and create civilisations under that form of government.

It began as a way to patch up civilization after the fall of a large empire (Roman in europe and various other in japan, china and russia, feudalism is "global" and not confined to europe, most didnt start during middle ages)

Answer 2

The lords ruled and owned the land and many of the developments on it. The serfs paid to farm and use those developments (like mills).

The other side of it was that the serfs had no organization or protective structure. The lord would protect them. He would often, with his troops, put his life on the line to protect the serfs from invaders, raiders, thieves, etc. The lords would enforce justice, settling matters between the serfs.

Some may call it a one-way deal, but both sides had a duty to uphold to the other.