1- Made of- where the material doesn't go through much processing- a chair is made of wood- the wood is just cut. Made from- processed- butter is made from milk- the milk has been processed into something else
2- If you mean the state something is in, then 'in bad condition' would be the natural choice. 'Under' can be used with the idea of 'circumstances'.
3- In the corner- inside a room, enclosed space- on/at the corner outside. I'd use 'at' for a tempory position- I'll meet you at the corner, and 'on' for a fixed one- my ouse is on the corner.
4- cause of- reason for something. cause for- I'd use this with a different meaning, where 'cause' means something worthwhile, so something could be a cause for a charity.