1. How does the Gita describe the notion of the "self"? That is, when this author says "I" or "you," what does he apparently mean?

The "self" is described as a permanent individual, which eternally interacts with other selves. The "self" has no form, is spiritual, eternal and gives consciousness to bodies that would otherwise be dead. The "I" and "you" refers to the owner (self) of the body.