Why do Christians believe in the Holy Trinity when the concept seems impossible? Why do they believe Jesus is a God? Can a human become a God?

The basic answers to all of these questions are the same. First, Christians believe these things because this is what their scripture says.  Second, these things are no more or less impossible than the beliefs of any other religion.
In essence, every religion believes in things that are impossible.  If these things were possible, they would be part of the natural world, not part of religion.  For example, let us say that you believe that there is one god, who is a being who has always existed and who created the universe.  How is this believable and possible?  How can a being exist without having been born at some point?  How can a being make things (the universe) out of nothing, simply by willing it to be so?  From our perspective as humans, these things are impossible.  If we believe that they are true, we believe them solely because our faith tells us to believe them, not because our reason tells us that they are clearly true.
If we accept that every religion teaches us to believe in the impossible, then the “impossible” aspects of Christianity are not hard to accept.  If Christian beliefs seem impossible and unbelievable to you, it is only because you have not grown up believing they are true.  If we can accept that a god could exist without having been created, what is so strange about saying that there is a god who has three parts and yet is still one God?  In general, religious belief is not subject to reason.  We cannot prove our religious beliefs are true or false and we cannot say that someone else’s beliefs are unbelievable.  All religious beliefs are unbelievable and impossible unless you happen to share that particular faith.