What makes a mustang start shakeing when you crank it and its not bad when I go 35 to 50 mph?

My2000 ford mustang all of a sudden start shakeing real bad i took it to a auto parts store and tested it all the codes good i looked for vac. Hoses & made sure my sparkplug wires were on i'm going to look at them tomorrow! I had this car for 6 years never had any trouble with it? I thought it was motor mounts, Will the Cadillac converter make it vibrate & shake my steering wheel, seat, rattles the dash and the inside of the car! It just started 2days ago but the faster I go the better it gets but when I slow down and stop it shakes and I haven't drove it much but it getting worse by the day? Please someone tell me what to do

The Catalytic Converter is part of the exhaust, and unless you have a clog in your exhaust, it's not likely to cause a problem. The problem isn't in your tires, but is in the engine, since it will run rough closer to idle and not when the engine is running faster. The same condition will exist if you sit with the engine in neutral and increase the fuel to speed up the engine. Your motor mounts would possibly cause the engine to rock as the crankshaft spins, which usually is worse under load - higher speeds rather than when idle or lower speeds. Motor mounts will not cause the condition you have explained.

It may be timing, but is more likely a fuel/air mixture which involves your fuel injectors, which may be partially clogged on one or more cylinders which may cause the engine to run rough at lower speeds. Fuel or air filters may be worth investigating
Spark may be the issue, which may be coil, plugs or wires one one or more cylinders, but not very likely.

If you're not mechanically inclined, your dealer, or certified mechanic should be able to find and fix the problem within a few hours.

The codes in your engine are really about part failures, which would usually cause a dashboard light (the check engine or wrench) to illuminate. Running rough is a common indicator that some adjustments or tuning needs to occur, not related to a parts failure. Some parts may be required, but mostly tuning…

You may need a main ford dealer. Bear in mind at that age of car not all codes show up and not every garage has full access to full codes generated. Sounds as though we have a major issue. Since its engine shaking so badly would suggest incorrect firing. Possible fuel air mix/ignition side.
technician is best way to investigate and resolve.

It sounds like you might have slipped a steel belt inside one of your tires its real ez to check there will be a ripple and of course its usually on the inside you can have some one follow you and they can see it real ez this happens when you rotate radial tires from one side to the other rather than front to back as recommended or used the steel belts "seat" one direction so when you reverse then they'll slip past the seat and shift. Its a very dangerous occurance as with all the vibration head on collisisions occur frequently but it feels like vthe whole car is junk like your describing