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These word pairs both seem to mean "Convenient/Inconvenient". But what is the difference between them and usage cases?
From looking at their kanji and a few example sentences, this is what I've come up with. Is this correct?
都合 means more like circumstances or condition. 都合がいい would literally translate to the circumstances are favorable (on a particular day), which makes the meaning of "that day is convenient (favorable) for me".
便利 (as suggested by its kanjis, 便 - convenience; and 利 - profit, benefit) means advantageous/profitable convenience, i.e. useful or handy. A situation will be favorable and an object would be convenient.
So looking at your examples, they seem correct.
