the fan exhaust duct is already in place, it's outside the drywall so I have to later fix them in place and cover them up with plywood.

what do you mean how to run the electrical? I just take it from the living room?

I heard Panasonic ones are more expensive. Tomorrow I'm getting an 100CFM inline duct fan and grille and try it out first. I have recently moved a thermostat across a few studs, but I haven't added switch + fixture before. I watched a video yesterday and will watch again and take notes so I don't mess up the electric.

The main problem is how do I connect the grille to the vent? It's difficult to have an elbow inside the 3" ceiling space and if I have it on the wall I might as well just use a larger CFM wall-mount

the bathroom is below another floor. I am not too confident to cut through the sheathing, fearing that it is the heating vent or something else important.

is the electric same as an exhaust fan, with its own switch and everything?
EDIT: I am seeing a lot with a plug

it's ground floor, but thanks

If I want to go with the 5.25 inch tall fan, that would be too much right? Lowering by over 2 inches below the ceiling? Actually the hole isn't big enough for me to test placing the fan in place, but I'll enlarge it tomorrow (for the 4 inch tall fan).

The electrical I have managed to run through the hole along the joist to the other side of the bathroom.

Thanks for your reply! I deleted my previous comment as I now understand what you mean. I will definitely keep this in mind.