Kant's moral philosophy is extremely complicated, but its core principle is the autonomy of the will, i.e. the capacity of reason to determine the will independently of any external incentive. The implication of the autonomy of the will is that the fundamental principle of morality cannot have its ground outside of the will. For example, the fundamental principle of utilitarianism is the maximization of well-being, but well-being is an incentive external to the will, so it cannot serve as the fundamental principle of will, and utilitarianism cannot be the fundamental principle of morality.
What does emerge as the fundamental principle of morality is what Kant calls the categorical imperative, which has various formulations, the most famous of which is the formula of universal law: act only on those maxims (roughly, plans of action) which you can at the same time will as universal laws. This means that any maxim which you propose to act on must pass two tests to be permissible: the contradiction in conception test, and the contradiction in volition test. In both cases, the question is whether it would be in some sense self-defeating to will your maxim while also willing that everyone else act on the same maxim. To test for a contradiction in conception, you ask whether it is possible to even conceive of a world in which everyone acts on your maxim. Maxims of false promising are one example of maxims that violate this test because if everyone made false promises, nobody would believe anyone's promises anymore--promising would effectively cease to exist--so your own maxim of false promising would be impossible. To test for a contradiction in volition, you ask whether you could will that everyone act on your maxim while still willing that you yourself act on it. Among others, maxims of universal nonbenevolence, i.e. never helping others, fail this test, because everyone needs help at some point, so you can't will that nobody ever help anybody else without willing against one of your own essential needs.
As for your three kinds of determinism, they are all committed to the proposition that at least some events are determined by states of the world prior to their occurrence. They differ in the cause of the predetermination and the type of events that are predetermined. Physiological determinism holds that mental states are determined by physical bodily states; psychological determinism holds that mental states are predetermined by other mental states; and theological determinism holds that actions or events are predetermined by god.