Careful! Some versions of the 3850 take a 6-pin power connector, but others need an 8-pin connector. I believe most of the AGP 3850s were 8-pin, because AGP slots deliver less power directly from the motherboard than a PCIe slot. (Similarly, a lot of AGP 4650s need a Molex or a 6-pin connector, while the PCIe versions need no external power connector at all.)
So, double-check your card and make sure you get a power supply with either an 8-pin or at least a 6+2 connection if that's the case.
Also, to answer the OP's third question -- if you have onboard video, you will often have to disable that in the BIOS when you install a new card. Some boards will autodetect, some won't. But on older motherboards (which is what I'm assuming this is), you usually have to do it yourself.