He is God. He does not change, and he is always right
God promises us eternal paradise if we follow according to his will. God is moral not immoral.
It raises some problems; it makes morality arbitrary. It opens up the possibility that immoral acts might not be wrong if God said so. Kierkegaard pointed that out in Fear and Trembling. Second, if morality is what God commands and forbids, then God invents morality. But if God has no independent reason to command what he wills, than morality has no rational structure.
No. God isn't really a source of morality. Morality emanates from a society's desire to live comfortably and promote the safety and interests of it's citizens (or those with authority). The only way God could establish morality is if he promised people unrealistic gifts for their loyalty, like riches and eternal paradise; since God cannot provide those things to people realistically, his impact on morality is minimal.
Does God command morality because it is morally right, or is it morally right because God commands it?
I believe in God and objective morality, but the divine command theory loses to the euthyphro dilemma. Is an action good because God commands it, or does he command it because it is good?