1) No because it doesn't convert anything, it forces the PC to send the correct resolution/frequency (via the EDID protocol).
To make it short (and certainly approximate) , EDID is a communication system between a (recent) display and a video device where the display declares its supported resolutions to the video device, so that the video device sends the best/compatible signal that it can send. Arcade CRTs don't have this EDID system. So the VideoAmp, pluged between the video device and the display, emulates the display side EDID communication. You choose the resolution to be declared to the PC and the PC (or any EDID compatible system/OS that can send the desired resolution) sends it.
Unfortunately your 15k or 31k arcade systems won't be EDID compatible.
2) There is only VGA input, as the cable has to carry EDID communication (which is not possible with a simple RGBS+GND cable). Display Port, HDMI, DVI can be used if you add a DPtoVGA, HDMItoVGA, DVItoVGA adapter that lets EDID through. For HDMI, it has to be a modded adapter, that njz3 and bandicoot can provide.
I hope I didn't say too much nonsense.
They will correct me if I did