The answer is: all of the above.
Creative writing is a very subjective process that has no clear-cut dimensions. To characterize, or give life, to a character, the author can make use of as many literary tools as the author wishes. By showing what the character does, the reader can form an idea of the character´s personality, intentions, desires or motivations. Another way to do it is to have the narrator describe the character´s character in a straightforward manner. Yet another way is to deepen the reader´s understanding of the character by likening the character to some form of symbolism or imagery. Finally, the author can rely on the use of other characters´ reflections upon the personality of a certain character in order to make this character more robust. It does not matter if what other characters say about that one character is accurate or not, it builds upon the plot line and the character itself, from the point of view of the reader, and it can be expected that a resolution and a final picture of the one character will eventually arise as the one (though perhaps versatile) image of the character in question.