In not Dark Yet, he says he doesn't know why he should even care which leads me to think about the idea of depression. He knows it is getting dark but its not there yet and doesn't seem to me that he wants to try and make anything better. Also the tone of the song gives it this kind of giving up feeling, like something is coming to an end and he is accepting.
In Trying to Get to Heaven, I think that it is just talking about trying to live a good life and get into heaven. It is just one man by himself wandering through life wanting the most out of what he has. He also seems confused about what is "alright" which is part of why he is traveling the world trying to live a fulfilling life.