Your bathroom fan is likely a PM type DC motor (even if the field winding is an electro magnet) this means it has brushes and makes sparks, sparks are RFI (Radio Frequency Interference) Television is a form of radio so that could be the cause there.. There are cures starting with soldering a set of 2 or 3 disc ceramic capacitors (.1, .01 and .001 uF should do it) across the fan motor terminals.
Lights: a good old fashion 1141 type lamp with a nice hot wire, Kind of clean RF wise.. Modern LED's not so much and 12 volt florescent likewise no so much, Both of those can generate RFI as well... I know one of my Florescent lights takes out my ham radio rather nicely.
It will, eventually, become LED, which are easier to filter.