Hi,
ad 1. yes, they will, Angry Birds contains only XML file with links which are called and the content is downloaded from internet (adverts)
ad 2. do not know what "data network" is, but if you mean data enabled for mobile site then yes, turning it off will cause no access by mobile site to internet
ad 3. this should not be possible, may be the content is in application data cache; just try to tap on it - if it will takes to browser and content will be read, you did not turn off every possibilities
And yes, if you will block all three possibilities in our Firewall, Angry Birds will not annoying you with adverts :-)