Aang was definitely dead for a few minutes. Here's the proof.
1. When Azula hit Aang with the lightning bolt, not only did Aang fall down, but the gigantic Avatar Spirit fell down too. I don't think that would have happened if Aang was simply wounded.
2. When Katara was healing Aang, nothing happened. His wounds stayed the same, and then Katara started crying. That means that Katara's healing didn't work, and the only reason that it wouldn't work is if Aang was dead. Seeing that Aang was dead and she couldn't do anything, Katara started crying.
3. Aang began to show signs of life after the arrow on his head glowed. The arrow on his head only glows when he is in the Avatar State. Therefore the huge amounts of cosmic energy that go into Aang are what cause the glowing. So perhaps the cosmic energy was still entering Aang, and that is what brought him back from death. He opened the last of his chakras after all, so the flow of cosmic energy into him must have been greater than ever, and because he is the avatar, that cosmic energy might have been enough to bring him back to life.
I think that all the previous Avatars are gone now, so Aang can't get anymore help from Roku, but Aang is the beginning of a new Avatar cycle, and he will still be able to enter the Avatar State and control the four elements. He might also be less powerful in the Avatar State than he would have been normally.