From your descriptions the thermostat and furnace should work fine together. The thermostat seems to be behaving like it has a 4 degree temperature differential setting. Check the thermostat setup for the differential.
If this is a new furnace and under the installer's warranty, the installing company should be told since the system they installed is not working correctly.
As for noise, if the furnace is close to the return you will hear the noise conducted by the air in the duct and the duct walls. If the ducting is round metal duct, you can inserts a short piece of flex ducting thereby isolating the noise transmission through the metal ducting. If you have the room and can make the flex do a gentle 90 degree bend, you'll help mitigate the noise transmitted by the air in the duct. Also possibly slide a piece of carpet under the furnace to help absorb motor vibrations, furnace installation safety permitting.