1.Can I connect the visualizer to my computer?

Airopie: Yes, it can connect to PC, Mac and ChromeBook with a USB Cable.

3.Does the visualizer have a light source?

Airopie: Yes it comes with a LED on the visualizer.

2.Does the  visualizer have any on board microphone?

Airopie: Yes it comes with a built in on board microphone.

4.My camera constantly disconnects/reconnects on its own. How do I solve this?

Airopie: Make sure your USB cable is securely connected and has enough room to let the camera move freely. This is to avoid the USB cable from tugging.
The USB port on your MAC/PC may have gone wrong. Plug in another USB device to that port to check if this is the case.
Try your USB visualizer with a different computer and see if the issue persists.