My 88 suzuki is difficult to start and runs rich. After it warms up it runs great, but with reduced power.

Check the catalytic converter. As the engine heats it up the gunk expands which will cause the problems you are explaining.

Did you ever find out what was causing this? I am having the same problem.

Sounds like the control module/pick up coil in the distributor is bad.

The Oxygen sensor is very suspect. it is easy to damage on install, even with the correct tool.

Put the old one back in and test the car...

Sounds like a vacumn leak. Gasket under intake plenum may be leaking. Be sure the pcv valve has the o-ring around it in the correct place also as it will set a code.

DIFFICULT STARTING CAR IN COLD.WOULD BE A THERMO - TIME SWITCH.THE THERMO TIME SWITCH CONTROLS THE AMOUNT OF TIME THE COLD START VALVE IS HELD OPEN BY MEASURING THE COOLANT TEMPERATURE AND UTILIZING A TIME FUNCTION TO PREVENT AN OVER RICH CONDITION.THIS COULD BE MOST OF YOUR PROBLEM.BUT SCAN IT TO SEE WHAT PCM CODE YOU ARE GETTING.

it almost sounds like the timing is off causing it to load up on fuel.

Check the exhaust manifolds. On a lot of the engines there is a little vaccuum operated valve that is supposed to help the engine warm up faster to reduce emissions. A lot of times it gets so rusty that it gets stuck and will make the engine run rough after it warms up. Had it happen on my 83 with the 307, so I disconnected and plugged the vaccuum line and made sure the valve was open. Also check for a stuck/bad egr valve or other vaccuum leaks.

check the o2 sensor, throttle body, vaccum lines, that timing and spark is correct and working on all cylinders( broken plug or wires), try the module on the distributor sometimes that can do it to but usally it runs good then gets bad as engine warms, to me is sounds like timing which also could be in the valvetrain or in the chain and gears in front... hopefully this gets you started in the right direction

check your cat convertor