Forget City Code (Permit$) on Owner DIY remodel stuff. If I done my research and feel comfortable and confident with my work, I do it. You can too. And I aint talkin Beverly Hillbilly fixes.
On my bath fan, I ran it vertical 4 ft direct to an outside roof vent, sealed both ends and used insulated tape from a roll, plastic and couple strips of fiberglass batts . Other than the Jet Engine fan I knew I was buying, Im good. No drips or moisture in fan or ceiling.
1st floor only option is thru an outside wall.
2nd floor thru outside wall or attic roof.
What was the question?