You choose a target creature for Glistening Oil as you cast it, just as you would with any Aura. If that creature is an illegal target when Glistening Oil tries to resolve, Glistening Oil will be countered and be put into its owner’s graveyard. It won’t enter the battlefield and its last ability won’t trigger.

The last ability will trigger no matter how Glistening Oil is put into the graveyard from the battlefield, not just when the enchanted creature is put into the graveyard.

Multiple instances of infect are redundant.