Yeah to my understanding, air moves its way to the top of the radiator, thus being forced into the overflow tank. The air is compressed, and any excess air comes out of the overflow cap. However not many bubbles, at least not enough that I would be worried about. Thermostat is working I believe..all the hoses in/out of the thermostat are full pressurized and get hot.
And cold air when the heater is on. It was cold as hell awhile ago and turned the truck on, blowing hot air after a few minutes, stood outside the truck, chit chat, then left to go home, a few minutes after driving the air coming out was cold..not super cold but I wanted heat, not natural air lol and then a few minutes later it started to get warm again. Thats also when my temp guage had a spike in temp, but never got close to overheating.
There is a valve that controls the air to your heater, that would be the cause of your air blowing cold then hot, then cold again. Your thermostat could be sticking in the closed position also.