Alrite, I've got a few interpretations of Hello.

Playground school bell rings, again
Day in and day out, it's the same thing...a young child, living her life (somehow I always see it as a her)...

Rain clouds come to play, again
Day in a day out, life is depressing...

Has no one told you she's not breathing?
This is where my interpretations differ. This person lost someone very close to them, and either isn't willing to admit it, or can't stand the fact that the whole world around them moved on, no one seems to care, while she (or he) is left alone, with that memory. Another is, this girl's heart has been destroyed...either her dreams have been crushed, she has no friends and is made fun of relentlessly, something. She feels like she is dying because there's no one there for her, she has no support. Something along those lines.

Hello, I'm your mind, giving you someone to talk to. Hello!
In the first interpretation (not willing to admit the loss), this person cannot move on without this person they've lost...and so in their mind, this girl they've lost is still alive. So they hold on to those memories because that's all that's left...or create an imaginary friend who is the person they've lost. Regardless, they can't let go.
In the other two mentioned above, they can't talk to society about their problems, they can't talk to anyone...so all they have left is themselves.

If I smile and don't believe, soon I know I awake from this dream
All smiles are fake...nothing makes them happy anymore...maybe soon they'll snap back into reality or overcome their problems, or at least put up with them.

Don't try to fix me I'm not broken
basically "leave me the hell alone" or "there's nothing wrong with me" in any event...this line is why I feel the last interpretation works with the lyrics more--there's nothing wrong with me, so stop trying to make me something I'm not, stop making fun of me for who I am.

Hello, I'm the lie, living for you so you can hide--don't cry!
In not willing to admit their loss, they're caught up in the world they created in which the person is still alive...and is hiding in that world. In the one where the world around them has moved on...the same could apply. In the last theory, the one I think fits the best, the person creates a world in their mind where they are liked by everyone, where good things happen to them, and they hide in that world...living in the lie in their minds, failing to see reality for what it is.

Suddenly I know I'm not sleeping
They snap out of the previously mentioned world they have created

Hello, I'm still here, all that's left of yesterday
All they have left is themselves...that world they created...although now they realize they've created the world and are now seeing reality for what it is, they have the choice to go back to that world or live in this one...they still have that world they created as a crutch to lean on if anything happens.