#1. (OK, fine) Yes Is it possible, You are good in writing? I think it is always at after good #2.
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mizansinha007You are good at writing.Good.
mizansinha007You are good in writingNo.
mizansinha007I have some problems in listeningPossible, but not really idiomatic. 'problem' is usually followed by an -ing form without an intervening preposition.