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I've been looking at some beautiful paintings that represent Krishna and would like to know some more about him. Why is he blue? Did he play the flute? Did he ever die?

Krishna is the origin of everything, so the blue of the sky is a reflection of His skin color. He is what color He is, and there's no material "reason" for it, the way there are reasons for why our skin is a certain color (pigmentation, chemicals, etc.). Someone once asked Srila Prabhupada, our spiritual master this question, and he replied, "Ask Him!"
What more can I say?:-)

Yes, Krishna plays the flute. He uses the flute as a means of communication. He calls the cows—each by their own "note." He also calls His devotees, who are very attracted by His flute song. Krishna also transmits knowledge via various ragas on His flute. He has many flutes—of various sizes and made of various materials—which He plays.

Lord Krishna is the Supreme Personality of Godhead. He is eternal, ever-youthful and never dies. He is always existing and always engaged in His loving pastimes with His devotees.

I hope that is helpful.
Sincerely
Laxmimoni dasi