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
Gets clogged
Yes if it is totally clogged.
Engine mounts
Yes, if it is clogged very badly.
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.
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.
Check your catalytic converter, as it rattles badly when the insides break apart. Get a replacement at any parts store. If it is welded in, you will have to cut it out, close to the converter on both ends, with a hacksaw or torch (be careful with a torch!). Use whatever reducers and clamps are necessary to make the replacement fit tightly, make sure there are no exaust leaks. Or, take it to a shop that does exhaust work.