I like to play my PSP at home quite a bit. When I do I plug in the AC adapter so that the battery power doesn't get used up unnecessarily. I see that when I have it plugged into the wall that under the system information it says that the power is being used from an external source instead of the PSP's battery. I take it then that the battery won't overcharge and it's OK to use it this way, or do I have to remove the PSP's battery when using the power cable?
It is fine. The PSP is just telling you that it is taking power from the outlet instead of the battery.