The character is a custom model rigged and imported into Unity, right? Not bad!
You should always be able to unwrap a cube or a rectangle in this manner:
http://en.wikipedia.org/wiki/File:Cube_ ... apping.png
In Blender, mark the sides to "cut" with Ctrl+E, Mark Seam. Then change the window to Unwrap Mode (Ctrl+left or right arrow a few times if you don't know how), choose the whole thing and 'u' Unwrap. Usually, after unwrapping, you want to choose the unwrapped UV areas, then go Ctrl+A, Ctrl+P (all parts to the same scale, automatically pack all parts).
It will probably look better if the hands and arms are all weighted to a single bone, so the cube doesn't deform at shoulders.
As you noticed, the light and the camera need more work.
The spot lights you could just turn down to a much smaller intensity (0.1?) and put them close to a wall. That will give the idea that the wall is somehow giving off light, which is easier to understand than an empty spot of air giving off light!
Even before you have the time to do the camera script, you can just move the camera it a bit higher and rotate it to point a bit downwards. That'd help a lot, already.
Also, turn the character so that when the player first starts, he immediately sees the first green point he or she has to collect. It might be on a small platform, so that the player has a reason to try and jump, and he realizes jumping is allowed.
The particle effect is currently looping. Uncheck the looping box, and it should stop repeating endlessly. A simple "hurray! you did it!" particle effect would be balloons. Remove gravity and find or draw an image of a balloon, and they'll fly away. If you want to get something cooler, do the balloons but also add a second particle effect that explodes in a shower of randomly colored confetti, and have them both activate at once.



