The heat shield on top of the converter may have broken loose. it can be repaired. If the rattling is inside the converter it must be replaced.
Replace it.Replace it.
More than likely the heat shield is cracked or loose. Repair or tighten it.
No.
Check that catalytic converter is not plugged
Engine mounts
Yes if it is totally clogged.
Gets clogged
Take your foot off the brake You may have either a misfire or a plugged catalytic converter. Is the check engine light on or flashing? Does it sputter or is there a loud throaty noise?
Yes, if it is clogged very badly.
There are a few things that might cause an air conditioner to make a rattling noise. It could be that the there is dirt and debris in the cabinet. If this is the case, cleaning the cabinet should stop the rattling. The reason could also be loose panels on the cabinets. The fan could also be bent and no longer straight.
Check for plugged: fuel, air filter, catalytic converter
Sure it is possible but it is not advisable. The heat shield is there to prevent heat from the converter from potentially getting the floor of the car so hot as to cause a fire. If it is rattling, a temporary fix is to purchase two large adjustable metal clamps and simply place them around each end of the converter and heat shield. This will stop the rattle, and protect the underside of the vehicle.