No. You need the CPU to run the code that makes the beeps.
Yes. Bad or missing video card or RAM would still generate beeps.
Pretty much, with one exception here. The BIOS can check the interface between the video card and the motherboard. It cannot check the rendering portion inside the video card. So you can hear the single short beep of a successful POST and still not see anything on the monitor.
Keep in mind that you do not need keyboard, mouse, drives or monitor to successfully POST.
Worst case scenario is just PSU, motherboard, CPU, and silence. Without known good parts to substitute, you really have no idea which components are bad.