The lights can be on the same lighting circuit as the room. No GFI protection is required unless the mfg requires it. VERY few do.
Almost all recessed housings (cans) and trims are damp rated. You only need a wet location shower trim if the light is subject to shower spray. Most simply install these trims regardless.
WHY would you run a dedicated 20A circuit to a bath fan???? Does it have a heater? If so then I bet the instructions call for not installing it over a tub or shower.
Also, WHY install it over the shower to begin with? There is NO difference in the venting efficiency if it is in the room outside the shower, especially a small room like you have.
Is the shower stall sealed off from the room?