Your car will still give trouble codes if there are any. But you said the light has never come on so there shouldnt be any. The check engine light does not come on for everything, only electrical malfunctions. And about your idling and engine response, there are shops that do a real fuel injection cleaning and you might also want to try to have your vacuum lines cleaned too. It is an older car and this should take care of your concerns

The service engine light will come on everytime it has sensed a trouble code, resetting the computer will erase the codes in it, but new codes that set will turn on the light again. They are known for the EGR (exhaust gas recirculation) valve sticking and causing a chuggle or choking condition, but get it scanned at a reliable parts supply store or garage to diagnose better. Best to just get a tune-up (especially fuel and air filters for sluggishness). If problem persists get it scanned for free at most large auto parts retailers.

There are a couple of thing that can cause drivability issue and not give you a check engine light. Like for instance, catalytic converter going bad. If by "reset the computer" you mean you disconected the battery, that does not erase codes in history. But is the light has never come one then probably you don't have any.

The answer is yes. How long it takes to come back up depends on what the problem actually is. You can reset the computer but the problem still exist and will cause the computer to throw the code back up as soon as it detects it and identifies what it believes is causing the problem. You could have something as simple as a clogged PCV valve or O2 Sensor being bad to something more serious like a leaking set of rings or loose timing belt. Before you reset the computer stop at an Auto Zone or Advance Auto and ask them to connect their code scanner and identify the code that is causing the problem. Most of them do that for free and that will tell you where to look.