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You mean сухо? сухой is dry. I think you must have copied something down wrong.

суко? Did you mean с*ка?

His signature could be correct (besides the soft sign at the end of живу), depending on the context.

I live at home. - Я живу дома.

I live in a house. - Я живу в доме.

Don't ask me about the cat.
не спрашивай меня о коте.

I couldn't figure out what you meant in the rest of them, that weren't already corrected.