Will atheists go to heaven?
Qur'an says there are good people everywhere and they will be judged according to their acts.
What is the Quranic definition of Kaafir?
One who denies the truth.
And what does Allah mean when he says "only deen acceptable to Him is islam"?
Deen is the way of life that brings about balance and peace to societies and anything else will not do so. Anything that enhances human rights, helps the needy, provides for all, is a part of deen. Anything else will bring about the opposite so is not acceptable to Allah or man.
Addendum, right acts will produce right results, but unless you are creating a environment that is conducive to all, good acts from those who are not 'in the right system' will help in the short term but not in the long term.