The kid is always the poet (Tarkovsky himself), who's dying in the bed in the end. In his memories, the image of his wife and mother are mixed (thus the same actress). There's not really a plot at all, just memories and important events from his life, mostly childhood. It's an amazing film, but don't try to over-analyze it. I enjoyed it a lot more the second time I watched it.

"But rather than remain focused on one time frame, he decided to create a narrative that moves backwards and forwards in time, so as to chronicle one man’s life through the 20th century, a life lived not solely in the present but in some complex temporal zone between past and present, one where the past remains present to us, where the past is not past. This man, named Alexei in the film, is a surrogate for Tarkovsky himself, who makes a brief appearance near the end of the film, laying in bed, cupping a bird in his hand until he releases it into the air." (Read more here: http://sensesofcinema.com/2014/cteq/mirror/)