Believe:

[athoughtfulman]

Is something that is not true a belief? Even though we 'believe' it is true?

I'm guessing you mean "believe it is not true"?

Probably not, though in the strictest sense of the word, you could argue it was a belief. However, I'd be more likely to label it as a negative belief or non-belief. Which is the opposite of belief. You can "believe" in something such as god or the tooth fairy, but it's incorrect grammar to say you "don't believe" in god or the tooth fairy. Non-belief is the more accurate term.

As for believe and belief. They are one and the same. Remember learning grammar in school?

A "belief" is a noun, and "believe" is the active verb of "believe". They mean exactly the same thing; they just have different uses.