Sumi is more like a corner inside (corner of inside of a room or a box for example) while kado is something outer, something protruding. For street corner, we use kado but never sumi.
Kabe is a wall inside a building, hei is a wall outside, a kind of fence.
Riyuu is the reason why, wake has much wider meaning, including sense, circumstances, how things should be/supposed to be, etc.
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edit: Oops, Mike san beat me.