I have a dual zone heating system. I set the upstairs to be lower than the downstairs however whenever the heat turns on it pumps heat upstairs along with downstairs even though the heat upstairs is significantly greater than the set temperature. Even when the furance is off I can hear water trickling in the pipes. I have forced hot water heating system

You may have a stuck zone valve, or lack of correctly placed check valves in the system piping at the boiler causing the hot water to circulate backwards through the upstairs while the downstairs is calling for heat.

I have to agree & will add you have air in the system. A system with no air will not exibit a running water sound.