Odd ceiling fan wiring, white in hot side of outlet
This white wire feeds a switch loop that provides power to the switch for the fan.  Unfortunately, there are several problems here:


This white wire needs to be tagged with black tape to mark it as a hot
It's not clear where the neutral comes from, but it's clearly not coming from the same box as the hot.  This is at minimum a 300.3(B)/310.10(H) violation due to the wayward neutral (and a great way to screw up things sensitive to magnetic fields), but may also be a much more egregrious violation due to someone abusing the ground as a neutral.
There's another junction box somewhere in this scheme that's doing something odd.  You'll want to find it before doing further fiddling with the circuit.