As long as your wifi is turned on and you are within range of a known(i.e. one you have already logged into) wifi network, your phone should default to the wifi signal over the cellular signal and you would not be charged for the data you use. Of course if this wifi signal is coming from a source which uses cellular data(i.e. mobile hotspot, jetpack, etc...) the cellular data from that source would be used.
As to signing out of AOL and Facebook, it depends on the settings you have set in those apps. If the app settings are such that you are receiving "push" notifications, you can be using data when not actually having those apps opened.