How do you remove a rusted dampiner pulley from an olds 91 98 without breaking it? also the car from time to time when pushes past half acceleration would stall. As of now the car will not fire and is not receiving a spark. The car will crank put will not fire and the only three thing we can figure is the crank shaft sensor, the cam shaft sensor and the igniton module.

It is held on by four bolts, remove them and tap the pulley to break the rust bond.

You have not shared what art of the country you live in, but I may be able to guess your answer.
All cars as old as yours are subject to brake failure, usually from leaking or rusted components.
A good inspection now should show you the rear brakes are bad, and perhaps the brake lines have rusted through.
Could also be a rear brake cylinder has failed, leaking out your brake fluid, and causing the brakes to give out when you needed them most.
Routine inspection probably would not have caught that, but having your brakes serviced every 7 - 10 years should have prevented it.
Lots of people do not do a complete brake service because it can get really expensive, though it would prevent your accident.
The acceleration problem is a whole different matter.
God bless your efforts.

if the hub is still on the crankshaft , the the correct way will be when the pulley edge lines up with all the other pulleys edges ( for correct belt alignment)
look at the bolts holes and you will see where the spring washers were on the bolt hole faces or the back will have no paint where it was on the hub

Apparently there is a tensioner that is not keeping the belt taught and it is not centered correctly on the pulleys. Or the pulley itself could be cracked warped or nicked.. Check out all the components carefully. A small nick or crack can cause the belt to chafe and run off the pulley and snap.

if we can't trust mechanics, then "there will be no old cars."
(imagine, that, only new cars run,,, never old......imagine that)
the car is old, 23 years old.
most old cars come in to the shop and there are 10 major issues
not ever corrected. the owners don't want them fixed so we send them away,
find a good ASE shop,. no ASE shop needs to lie to you or cheat you
they are pros. and as such do not need to cheat you as they will be
fantastically successful just being honest ( a shock , huh )

we can not feel your throttle cable here in the internet cloud.
but if the cable sticks, and is stuck at near wide open throttle
the engine fuel system is cut. this is a FEATURE. to unflood engines.
(operators guide (lost) explains this)
why not get the car inspected,
and do expect there will be many problems on any 23 year car
this is true with all machines that old. not just yours. its called,
entropy. in the end , its all just a rust pile..
yours truly , mr. sleazy mechanic

The old trick is to cut the current belt in half along its length, then remove the front most half of the old belt. Slide the new belt up to the remaining half of the old belt, then cut of the old belt and push the new belt fully on to the sprockets.

They are sometimes installed with threadlock compound which makes it very difficult. How big and powerful was the impact wrench? Is there scope yet to hire a really huge one?

The bump method is a last resort because it puts the flywheel ring gear teeth at some risk. Break one of those and you are up for expense.
.

If it has a belt, it can be changed without upsetting anything. Take a carpet knife and slice the belt in half along the length of it.Cut the front half and remove. Take new belt and fit over the front half of pulleys. Cut other half of old belt off. slide the new belt all the way on until in correct posistion.

easiest way to change a timing belt is to
first slightly slacken off the belt tensioner
carefully cut the old belt in half along its entire length while it is still on the engine.
remove the outer half only.
place the new belt on the pulleys up against the inner half of the old belt.
cut and remove the inner half of the old belt.
push the new belt fully into place.
re tension the belt as specified.

Depending on your years they will twist out or pull out. And about half the times they break. If it does you can get the rest out with needle nose pliers.