Hyundai Repair: 2000 Accent Rough Idle / Stall, technical service bulletins, engine temp

Question
I bought a 2000 accent sohc 12v 1.5l and have recently experienced problems with the car after it heats up.

Almost directly off the lot I had to replace the fuel filter. I could not blow through it. So I suspected that it would fix the issue of stalling. Unfortunately to no avail.

The check engine light never comes on (nor flickers) The engine temp seems normal. However after the engine temp reaches normal the car begins to die while idling either in drive or reverse, however oddly enough in neutral or park it seems just fine, though the idle jumps to about maybe 1000 or a little above. While idling in a drive gear or reverse I get a very consistent purr with a what seems like a chug or it's attempt to die every 3 seconds or so. The RPM needle also drops a bit, maybe to 500 then shoots back up to 800. And it is during these little chugs that It commonly stalls. I have adjusted the idle up a bit to about 1000 in drive and still notice the chugs but I don't need to restart the engine in the middle of the intersection.

I've thought Of replacing the PCV valve because it's cheap... I'm also thinking of replacing the fuel pump.
I have replaced the fuel filter, plugs and plug wires.

I will note that I have also noticed that I've had to add oil recently because it had run low. But this could just be a small leak and coincidental.

I would appreciate and insight into this, I'm not very familiar with import engines, my last car was a 5.0 V8 in my Thunderbird, probably not very similar!

Thank you so much for your time!
-Mike

Answer
It's difficult to say what your problem might be since there are so many possibilities.  Here's what I notice.  The idle in park and neutral appears to be a little high, while the idle in gear appears to be at least intermittently low.

I checked the technical service bulletins and saw nothing specifically relating to your symptoms.  Here are the things I've seen fairly frequently that could be causing your idle/stalling issue:
1.  Leaking PCV hose.  
2.  Air intake bellows not secure on throttle body or air flow sensor.  
3.  Throttle position sensor problem.  In the early stages, I've seen this set a trouble code but not occur frequently enough to turn on the check engine lamp.

If you don't find anything with the intake bellows or the PCV hose, it may be worth your while to have the diagnostic trouble codes checked even though the check engine lamp is not on.  You might also try wiggling the TPS connector to see if it makes anything abnormal occur.

It's doubtful the low oil level has anything to do with your idle/stalling condition.