Low rpm like that does make the oil pressure gage drop to zero because the oil pressure pressure switch is about 8 psi. Low idle will trip it to a zero psi indication = NORMAL at THAT low of an idle.
Focus on the low idle problem.
The IAC controls idle.
A simple test is to disconnect the IAC and see if idle drops. If it does, the IAC is at least working. That doesn't mean it isn't STICKING.
With your newly installed engine, you may also need to let it relearn its idle strategy.
Let it idle for 4 minutes in each of the following conditions:
Engine must be at operating temperature:
Park
Drive, foot on brake pedal the whole time.
Park with AC on
Drive, foot on the brake pedal the whole time, AC on.
If it has a clutch, you only have to let it idle with foot on the brake and again with the AC on.
It's best to do this after resetting the PCM (Disconnect battery, touch the removed Negative cable to the Pos Battery post still connected to the battery. Or simply turn on the headlamps with the battery disconnected. Either method works).
Another possibility is that you have a vacuum leak and the PCM is trying to compensate for it. Make sure the tube from the air filter box to the throttle body is tight and has no holes in it!
You can clean the IAC shaft with a solvent and then whack it against your palm so the plunger thwocks as it slides along the shaft. Again, the IAC contols idle by metering a certain amount of air to maintain idle. Another thing to check is that the throttle body plate is fully closing and clean. Do not adjust that unless you are going to probe the TPS center wire for proper voltage with the plate closed, less than 1 volt. I think .96v is optimum, but you should look up the TPS test and do that.