More than likely the heat shield is cracked or loose. Repair or tighten it.
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.
No.
Check that catalytic converter is not plugged
Engine mounts
Yes if it is totally clogged.
Gets clogged
Yes, if it is clogged very badly.
Check for plugged: fuel, air filter, catalytic converter
A bad catalytic converter and stopped up muffler will slow down the car. The catalytic converter is under warranty up to 84,000 miles, if defective. If you ran over a speed bump and damaged it, you have to replace it. You can buy a lower catalytic converter for $120 from advance auto parts.
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.
That is possible.