After I finished the MQ in Skyrim (the same week the game was released), some dragons started to not attack me, they simply circle around and fly away. I searched all over the internet for some fix or even the reason this happens, and some people said this is not a bug because "some dragons are just like that". Is that really true or this is a bug? On another topic, after I finished the MQ, the dragons started spawning a lot less than usual, is that another bug?

You finished the MQ, of course dragon attacks are going to lighten up Alduin is not forcing them to fight. And yes some dragons are supposed to circle around you and then fly away, its not a bug.

http://elderscrolls.wikia.com/wiki/Random_Encounters_(Skyrim)#Complete_list