Why my vito wen i pull o way fast cat off and smoke white

Have you checked for vacuum leaks? Poor idling when cold that gets better when the engine warms up, or at higher RPMs are symptoms of vacuum leaks. Check all hoses and connectors. If it's a manifold gasket, you will want to use a smoke machine (check when the engine is cold).

Leaky injector

White smoke is water vapor and in this cold climate it is normal. Strong gas smell is not normal although you may smell some while engine is warming up. Bad cat converter can produce smells, but usually more like rotten eggs. If engine is running rough and seems rich, check coolant temp sensor. Bad converter can cause stalling too. Otherwise, idle speed is controlled by idle air contol motor which can get dirty and stick. Any codes set?

There are several causes for this, including the above.
Check the spark plugs and coils/wires. Lose or worn parts can cause this. If the spark plugs have thick black residue, you have an oil leak. A flat black powdery residue is too much air. A thick crusty white/yellowish residue would be a coolant leak.
If it is blowing blue or white smoke when running, the you have an oil (blue) coolant (white) leak that needs to be fixed. Normal smoke is grayish in color.
Check all the vacuum lines as a leak may be the problem.

Park it and forget where you left it. Or if you have any mechanical skills or inclinations, you could do some basic tests, but avoid the dangerous driving test - do this with the engine running if it needs to be running, but stationary.
It sounds like it could be the catalytic converter is getting clogged. It blocks the exhaust from going out the tail pipe. When the car is completely cool, if you thump it pretty hard, or grasp and shake it, and hear any rattling, then it is damaged and probably blocking your exhaust. If it sounds good, you could next open the exhaust somewhere ahead of the cat converter, like pulling out an oxygen sensor temporarily, or disconnecting the exhaust somewhere. Then run the engine and see if it noticeably improves. That's a bad cat.

Last, which probably should have been first, is check for trouble codes. Most important don't let repairs bankrupt you.

white smoke can be water in the exhaust if you park with the rear end facing up hill it will store water in the cat and take a few miles to clean out. 2000 rpms is a bit fast. should be around 800-900 rpms. it could be a sticking idle control. take it off and give it a good clean out.

Valve seal leaks will cause an engine to smoke on start until the oil burns off. If a head gasket were leaking it would be smoking constantly.

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I don't know if it would cause the shaking and vibrations, but for the smoke it could be loose nuts or broken studs on the exhaust manifold -- when engine is cold check each of the nuts (there should be 8) to see if they are loose or missing/broken; you may have to remove a heat-shield in order to gain access

Do You Get An Engine Code
Sounds like A Cylinder Is Misfiring
Or A Valve Is Not Seating Good

sounds to me like your idiling too high