ronv;
I do not understand what the labels "panel" and "out" mean. Are they just bus labels?
Yes, They are just there so you can see which waveform is which.
What does Rser = 6 and 12.6 Rser=.05 mean?
These are the series resistance I assumed for your panel and your battery.
D2 I believe is there to keep the battery (v1) from discharging back through the solar panel when the battery voltage exceeds the solar panel voltage.
Correct
The positive side of both the battery and the panel supplies (?) the EMF to the emitter of a PNP transistor. (component Q1=part numberBCW68F)
Yes
R2 is used to limit the current supplied to the base as the solar panel voltage increases. This causes a forward bias on the base???? and stopping the flow of current between the emitter and collector????
The base is slightly reversed biased when the panel voltage is higher than the battery voltage.