Which front-end are you running? ie Fluidd, Mainsail, or Octoprint? I’ve only used a webcam with fluidd, but it was pretty much plug and play. Are you using a USB webcam, or a raspberry pi cam that plugs into the camera connector on the Pi?
The shaky table will definately affect your prints, it will result in ringing or ghosting. You can use Klipper’s resonance compensation to compensate for it somewhat, but you’ll get best results by reducing accelleration on the printer