Driving with out catalytic converter?

No. On any model that age, it is only there to clean up the exhaust. There are no electronic sensors or controls to monitor the converter's performance until all 1996 models. There should be no change in engine performance.

There's no way for me to know what all has taken place or if anything else has been damaged, but the engine doesn't really know or care what happens after the exhaust gas leaves the cylinders. Some engines are tuned to perform best when there's a little back pressure from the exhaust system, but beyond that, no further damage should occur.

You may have read conflicting information from other sources, but it won't apply to an '84 model. Specifically, the front oxygen sensor tells the Engine Computer what has taken place in the combustion process, then the computer makes fine tuning adjustments to the air / fuel ratio. If your model has, or had that front sensor, the computer won't be able to calculate those small corrections, so you could use more fuel than normal. Slightly too much extra fuel isn't bad. It helps cool the intake valves. Too little fuel, meaning running too lean, is not good if it lasts too long. Over time that can lead to burned valves.

Also related to newer vehicles starting with all 1996 models, they use a "downstream" oxygen sensor after the catalytic converter strictly to allow the Engine Computer to monitor how efficiently the converter is doing its job. That one has nothing to do with how the engine runs, except for one important condition. That being, ... When that sensor is missing or not performing properly, or is simply providing data to indicate a problem, those will turn on the Check Engine light, and set at least one related diagnostic fault code. The Check Engine light gets turned on when any fault code is set that relates to something that potentially COULD cause increased emissions. That, in itself, is not a problem as it relates to engine performance or damage. Where the problem comes is when that warning light is already on for a defect you know about, you will never know if a second / different defect gets detected. That could be a minor problem that can turn expensive if it is ignored, and of course, it will get ignored because you have no way of knowing that second problem has occurred.

A second way this can make a problem is when a fault code sets, there is always a long list of conditions that must be met for that to occur. One of those conditions is that certain other codes can't already be set. In this case, you would have a code related to oxygen sensor performance. That code will automatically cause the computer to suspend a number of other tests it runs continuously. That means any of many possible defects could develop and never be detected. This can be really frustrating for car owners and mechanics. You take the car for a diagnosis and repair estimate, and all the mechanic knows is the first fault code. He has to make his estimate for repair according to that. Next, when you agree to have that repair done, on the test drive all those suspended tests resume, that's when the new defect(s) get detected, new fault codes set, the Check Engine light comes back on, and we have to start all over.

That last problem has much less chance of happening when the first problem is diagnosed and repaired right away. It's when people wait for weeks or months that there's plenty of time for additional problems to develop, but often aren't detected.