Filling up in the morning , when it's cold, is supposedly when the gas is more dense. Probably technically true, but the difference would be infinitessimal.

Filling up slowly, this one might conceivably have merit, but I have to believe the pumps are required to be within a certain accuracy.

The logic for not letting your tank get below half full is that the gas evaporates into whatever space is in your tank. Again, probably technically true, but the air will quickly reach a saturation point where it can't hold any more gas vapor.

Filling while the tanker truck is there supposedly puts more impurities in your gas that get stirred up by the fuel being pumped in, but I have to believe that the pump's filters take care of this.