Ask about the attachment, not the device. The four things a landlord is actually worried about, answered before they raise them, plus what to write.
Adhesive hooks hold about 7.5 lb. A two-gallon pet fountain is heavier than that before you add the housing. The arithmetic no mounting guide does.
Mid-term, generally not. At renewal, generally yes. The exposure is not who owns the building, it is the date your term ends, and what to do first.
Only the deposit is ever in play. Landlords must itemize deductions, and in some states missing the return deadline forfeits deductions entirely.
Leashed, service elevator only, or carried with no paws on the floor. These live in house rules, which can change without your lease being reissued.