Yes - there are fans where the motor sits above the roof.
https://www.fansonline.com.au/exhaus...aust-fans.html
The whirly bird suggestion is a really bad idea. Whirlybirds don’t move much air - and you shouldn’t exhaust damp air into the ceiling space anyway - especially if you don’t have any ceiling space! It causes condensation which is bad for timber and not good for metal roofs either.
Also, make sure you have air coming into the room or an extraction fan won’t work properly.
Is the best place for the fan at the ceiling apex - or should it be closer to the shower? Get some technical advice.
To kill mould permanently, you need to use diluted vinegar and the ‘three buckets‘ method recommended by Choice. https://www.choice.com.au/home-and-l...g-rid-of-mould