You asked a question that I am actively pursuing in studies. I can honestly say that no one really knows the complete picture. We only know bits and pieces of the puzzle so far and no one has formulated the whole thing. I suspect that it is a question that will be answered over the next 50 years of study and research. Many people are working on it. There are over 26 different universities that have significant research going on in neuroscience, cognitive sciences, and related areas of several diverse fields of study, including phenomenological philosophy.
The idea of localization of abilities have clearly been identified for specific things like motor, vision, hearing, and linguistic understanding and speech. Other talents like music, mathematics, and the creative arts seem to be a synesthesia of sorts that blends adjoining areas of the brain.
Because of ethical reasons you cannot remove parts of people's brains for study, unless there are tumors that require it. So scientists often depend on lesions that occur by accidents or strokes and run volunteers who have suffered the lesions through a battery of tests. Using fMRI study of blood flow much can be determined what parts of the brain are active in normal people and patients.
Some functions don't entirely seem to be localized. The sense of self may or may not be localized. We know that consciousness is not a monolithic thing so we would expect parts of it to show up in diverse parts of the brain if it were localized. But excision of most of those parts doesn't seem to eliminate all aspects of consciousness.
Also after a stroke localized functions such as motor control seem to be able to relocate if extensive therapy is available.
The brain appears to be a malleable thing and it is an evolving thing. Most of the mental skills of humans can be shown to exist in lower level animals who evolved long before humans did. Most of the mental abilities that we have as humans were developed in animals which preceded us in evolution. We humans, however, have mainly accomplished the honing and refining of mental abilities that already existed.
A crow for example can count to about 5 but gets confused when you get up to 6 or higher. That is pretty good as most animals get confused above 3. Apes and chimps have abilities to develop limited language skills using sign language. It is clear that most animals have some sense of self, sense pain, and if they are social animals they all have empathy and a sense of morals.
The real problem you might have with terms like creativity, imagination, intuition, and consciousness is that they are metaphors and mean slightly different things to different people. None of those terms are really scientific and while they help us make generalizations in every day talk, often those extrapolations veer us off into wrong directions in our research on thoughts and we end up baffled by contradictions.