My question is clear: what is philosophy and why it is exist and why people still care about philosophy when we have science?
Historical note: Only a few centuries ago no distinction was being made between philosophy and science. Physics at the time of Newton, for example, was referred to as "natural philosophy".
Science is a particular method of acquiring knowledge: observe nature -> form a hypothesis -> make a prediction -> conduct multiple experiments -> confirm or reject. Scientific knowledge is one of the most reliable kinds we have, second only to mathematical knowledge.
Philosophy, on the other hand, encompasses any "knowledge" that could be obtained through questioning, speculation, discussion, reasoning, and not necessarily including observation.
In that sense, science is a very narrow part of philosophy. It is not concerned with (among other things):
the unobservable, e.g. claims of the existence of a god who never interferes with the universe
the unobjective, e.g. ethical question, which are very much dependent on the cultural background of who's asking them
the untestable, e.g. string theory is sometimes criticised as "unscientific" for beautifully explaining nature but not making any testable predictions about it
the unrepeatable, e.g. claims of miracles - one-time violations of the known laws of physics
Philosophy (apart from science) exists because of the human desire to pursue knowledge, even at the cost of its quality.