1) The peasants actually controlled the supply of food, not the other way around, because they worked the land and grew said food. If a Lord pissed his peasants off too much they'd move to another lord's territory and the lord would promptly starve.
From my incomplete reading of history, from the formation of the Feudal system till it started to break down after the black death - serfs/peasants were definitely not allowed to move, in fact there are many documented cases of Lords going after their 'people' to drag them back, punish them and put them back where they belonged. In these early times another Lord probably wouldn't have accepted them - unless they were highly skilled (unlikely as they were only serfs) as this would have set a bad example to their own serfs. The only other option to a person bonded to a Lord to escape at the time would be to go Outlaw - but then you could be killed on sight. It was the labour shortage of the black death that caused a buyer market for labour that helped to destroy this particular practice.
2) Peasants had rights, and a Lord's control over them was limited, sometimes quite dramatically (for example peasants in medieval England worked less on average than people do today).
True, but a happy serf is a productive serf as many Lords probably found and therefore good to have rules and privileges. But at the end of the day the serf owed service to his Liege, not the other way around.
3) Most lords couldn't read, and in that regard were as much at the mercy of those who could (the church) as peasants were.
A good point, but then again the nobility were free to move about, get news and hear new ideas and regarding reading - for example - if they needed to win a law case they could easily employ someone who could read the law/deeds whatever and win their case to their satisfaction. A peasant with a small strip of land, a cow and a few pennies just wouldn't be able to do that.
4) Lords had zero control over religious doctrine or freedom, and indeed the church had an enormous amount of power over them.
Everyone from King down was straight-jacketed into this one - but ultimately the church sided with the nobility - because they could get lots of nice things from them: Land, indulgences, concessions, secular power...
And powerful nobles do seem to have done anything they liked anyway.
Yes different countries had different systems, so I'm thinking mainly of Britain/England but you can generalise a bit to other nations.