Is it possible for electrolytic capacitor to develop a short in one way only?
It sounds like the capacitor is functioning correctly.

Large capacitors are normally polarised with positive/negative terminals, so they only work one way which is why you not getting a short in one direction.

The reason you appear to have a short in the other direction is because the capacitor is not charged, and your multimeter is charging the capacitor as it reads the resistance. If you held your multimeter on the capacitor for long enough it will become fully charged and your meter would change to read an open circuit. Don't bother trying this with a 1 farad though, it will likely take a long time.

So it sounds like everything is good with your capacitor.