There is nothing inside a current dependent current source. It is not a physical entity. It is a mathematical device only. In this case, the collector current is dependent on the base current. The proportionality factor is beta, which is the transistor's current gain. I gave you the equation in a previous post, and a link to a more complete explanation.
The diode is there to represent the base-emitter junction, which has a forward voltage drop of ≈0.7V, but is actually a nonlinear function of base current
The diode is there to represent the base-emitter junction, which has a forward voltage drop of ≈0.7V, but is actually a nonlinear function of base current