I don't believe in the Christian/Judaic/Muslim god. Nor do I believe the universe was created five minutes ago.
However, my budding understanding of philosophy tells me that none of the above can be disproved. We have to accept the possibility that the universe is nothing but a computer program. And, as others have pointed out, there are different ways to define "God," some of which resonate with me.
But your reference to God was apparently just an example framed by your larger questions.
1. Is it possible to stay completely unbiased?
For all practical purposes, I think it's impossible for "normal people" to be unbiased. People who are into Eastern religion, meditation and the search for Nirvana might be capable of achieving such a state.
2. What is a good balance between the pursuit of truth and stay happy?
As a political activist, I learned long ago that truth can be a very painful thing. On there other hand, ignorance can be equally painful. So I pursue truth in the hope that I'll some day find some magic answer that will improve my lot (and hopefully help others at the same time).
As far as balance goes, most people need some form of escape from life's drama, and if you're constantly brooding about social injustice, war and climate change, you're probably acutely aware of the need for a respite.
So a good balance might be as simple as taking a break from philosophy and taking a walk, watching a movie, etc.
Of course, that's a practical answer, when you were probably searching for a more philosophical answer. One form of balance I find very helpful is humility - accepting the fact that a) there may be other options, and b) it's possible that the ultimate answer is beyond your comprehension.
For example, I've been doing some research on determinism, a belief that pretty much nixes free will. Some people believe we live in a deterministic universe and others don't.
Though some may not agree, it appears to be nearly impossible to prove it either way. So I'm resigned to the idea that a) there may not be an answer to this puzzle in my lifetime, and b) if some astro-physicist solves it, it could be beyond my understanding.
In the meantime, my biases prompt me to embrace free choice. I prefer to believe that free choice truly exists, even if there are nagging doubts in my mind that it could be an illusion.