Use any email address for imessages and facetime.
If you already had it working and now it isnt , even though https://appleid.apple.com/ says you are verified with the green tick , don't believe it necessarily, on your email address in there add a number on the end of it or change it slightly so it is bogus then apply so it will send a verification email , then revert it back to your real one and apply and get it to send a verification email to yuor account , for real this time , verify and imessages should just work.
I have a touch and an iphone working just fine on the same gmail account BUT it was turned off and I could not re activate whatever I did including dns 8.8.8.8 , logging out of itunes , date check , network reset , etc etc etc. I then wondered if the green tick saying verified was still valid in my apple id so did the above and voila.
It was VERY annoying and there seemed to be a heck of a lot of people with the same issue with the incorrect apple id or password message which was not correct, even going to extremes like reset network or rebuilding.
Yours may not be or by now you are fixed but hopefully this will show up in peoples searches that are having issues re-activating imessages.