Siam and Tigerkhan both gave really good answers. I will try and answer your questions specifically, although I am often poor with expressing things very clearly. So, I apologize in advance and I hope that my words do not come out wrong and unclear. Also, I am not a Muslim, so my answer does not reflect any opinion or line of thought that might be held by one.
I have recently started reading the Koran and I've noticed that the principal issue therein is belief in God. The actions based on that belief appear to be issues of a secondary nature.
I don't believe that any actions are of a secondary nature. Actions come out of love. Love for God. Love for others. It is not enough to simply believe in God. Even Satan believes in God and knows his words. It is more about KNOWING God than believing in God. And knowing God is about having a relationship with God, accepting his love for us and showing his love to others. God wants to have a relationship with us.
Actions stem from love, not belief. Often a drunk driver believes that driving drunk is dangerous and should not be done, yet he does it anyways. It is not uncommon to hear people with a vice tell others to never get into it-- yet they continue it themself. Belief alone is not enough to cause an action.
What is the purpose of believe other then to dictate our actions? What is the added value intrinsic to belief? Why does God care about being believed in?
See above for belief and actions. There is a line from a song that I enjoy and it says "Love is not a feeling, it's an act of your will." If you truly love, then will you act.
God cares because he loves us. He created us. He breathed life into us. Would you make a child and then discard it on the curb and shove it aside? God desires that we all come to know him.
Do your actions not define the quality of your character? If so, does it even matter (or would it matter to God) which belief (islam, christianity, atheism) inspired those actions?
I would say that actions, in some respects, do define a person's character, but they alone do not define it. Siam, above, mentioned intentions. Someone may appear to me doing good and acting in love, but in reality that person's intentions may not be right. The intention might be self-serving, for example, and love is self-sacrificial. Actions are an outward manifestation that character is often assessed from, but actions alone do not define character. I would say that it takes time to see true character.
Personally, I do not believe it matters to God which religion one follows; although, I will say that it would be impossible for most religions to have a relationship with a God that they do not worship nor believe in. How can they love God or show God's love, when they do not KNOW God? So, when I say that religion does not matter, it must not be taken too loosely. Religion, and religious teachings, are how we discover God and learn more about him, so in some ways, religion is important. As others have said-- there is only ONE God. Unless someone has a relationship with God, then he does not know God. And if someone knows God and loves God, then there is a desire to follow his teachings and to display his love.