Does a 88 pontiac sunbird have a caddiallac converter

all cars other than hondas after 1973 are required by law to have them. for the first 10 years or so after the EPA regulations came into being the CVCC motor that Honda made could pass emissions without a cat on it.

I assume you mean catalytic converter, and yes it does.

Even older cars have them.

its your timing, go to a shop and get them to change your timing belt. It is not your fuel pump nor is it your catalytic converters... when your timing is off it causes the stroke of the piston to not be in tune with the valves opening and closing. for example on the compresion stroke the exhaust valve might open a little causing loss off compresion (power) and pushing unburnt fuel into the exhaust

So the actual question is my car rattles and does not accelerate any more? first off it is over 20 years old secondly your lucky the old sun bird still runs third you still driving grandma is old car?

You mean catalytic converter? Yes, it does, along with EGR and/or O2 sensors.

Yes , all cars pretty much after 1973-74 time frame has a catylitic converter on them.

yes it does in part of the exhaust system