Not everything has a scientific explanation. Or even if it does, maybe some logics have not been discovered just yet.
That's true. Science doesn't explain everything, for most of them (if not all), not yet. But this is true for the things that we can scientifically theorize. We have life but science hasn't proven how the first living organism came to be (but they are close

). Or we have cancer but science hasn't cured it totally.
Do you only believe in science?
I do believe in science. But this is not like believing in a religion. I do believe in what science says because for something to be scientifically true, it has to be backed by scientific facts and methods.
Science does not believe in God. Do you also believe the same?
This is not entirely true. Or, let me say, this is not I would have put it. God, or any supernatural creator power for that matter, cannot be proven. As we prove things with scientific methods, my statement implicitly relies on science for this proof. If there was any scientific proof for the existence of any god, science would gladly accept it because it would be scientifically proven.
The scientific name for us is "homosapiens" and we are categorised under animals. Science believes that we humans evoulved from monkeys. Do you believe that you are actually related to the monkeys?!
If I may, the evolution doesn't say that we evolved from monkeys but it states your following statement, that we are related to monkeys, as we are related to any other living beings if you go back in time. Humans and other primates share a common ancestor, that is closer in time that our ancestor with, let's say, sharks. This is the only scientifically proven explanation of how simple organisms form more complex life-forms given enough time.
Everything may not have a scientific explanation but it does have a reason.
I am a rational person. I think and need facts and proofs. Assigning reason to various things is a common human trait. In this, children are perfect examples of this: they assign purpose to everything. To cite the famous example: "clouds are 'for raining'", "pointy rocks are 'so animal can scratch on them when they get itchy'". However this doesn't mean that they "have a reason". We perfectly know how clouds form, move etc. Universe is neutral to us and doesn't care about us.
And yes, everything that exists in this universe has a scientific explanation or can scientifically be proven. Science may not have all the answers yet but it is getting there. How else we would separate imaginary from real? As in my example of the beginning of life, science is trying to explain how the first living organism came by, or the age of the universe or what was there before the big bang, but those are all questions asked about scientifically proven things and not some imaginary things that may exist somewhere that we may not be aware of yet.
So I don't believe in things that cannot be scientifically proven and any rational mind shouldn't either.