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"Alive" and "living" are almost the same thing. "Alive" is an adjective and "living" is either the gerund form or the present participle of "to live." Both have to do with the property of being alive. The difference is that one is a description and one is an action. If you say "I am alive," you are describing a quality of yourself with an adjective (the quality of being alive); if you say "I am living," you are indicating an action you are performing with a verb (the action of living).

"Live" can be either an adjective or a verb, depending on how you use it. If you say "I am a live person," it is an adjective (it is modifying the noun "person"). If you say "I live," it is a verb (it is indicating the action of the subject "I").