If your downspout and exhaust are both 1) within code and 2) are not discharging onto the other property, you would not have to relocate them. However, obviously, if you are violating code, you could be required to bring them into compliance; and if you are discharging water onto another property, you may well be violating that property owner's (the city's) rights and they could potentially bring a legal action against you to require you to stop damaging, or polluting, or impairing the use of the adjacent property.