Can I run a 12 volt DC brushless fan underwater? (The fan is about 2 inches wide) It is a standard fan
It should work fine in de-ionized water but for tap water or pond water you should probably coat the electronics to insulate them from the water.
It will probably work, but you won't be doing it any favors by running it submerged. Water will sap quite a lot of power, and the bearings might not appreciate being submerged.
When you say 'fan', do you mean something designed to blow air? Are you running that under water too?