What was with that burned-looking picture of a tree on the barn wall?
Samara created it by either physically burning it with her hands (recall the burnt impressions where she grabbed Rachel and Aidan) or using her powersof thermography. This ability, as mentioned above, allows one to create an image using the power of the mind. As for the tree, this was naturally significant to Samara in that it marked the location of her demise. The images on the videotape would indicate that Samara had powers of foresight; she was probably aware (at least on some level) of her own death.