Can my neighbor live in a shed, RV, or camper in the yard?

No.

Shed: Manufactured storage structures are not permitted for occupancy. Manufactured storage structures mean any pre-fabricated structure designed for storage and not for habitation, including any structure such as a shipping container or pre-fabricated building that does not satisfy the appropriate codes for a residence. (Manufactured Homes Ordinance Ch. 26)

RV/Camper: Using a recreation vehicle as a permanent residence is prohibited in any zone or on any lot except in an area zoned RM (Residential Multifamily) and adhering to those specific requirements (Art IX Sec.902.39). This is not to prohibit the use of a recreational vehicle for temporary housing by a property owner while a permanent residence is under construction for which a building permit has been issued by the Planning Director (Article XIV Sec.1413).