hashkafah philosophy - What was the value of the Rishonim's philosophical inquiries about God and the world?

Many Rishonim used the philosophy of their time or previous times to 'prove' God's existence and/or learn about the nature of the world.

1- Why did they do this? (Is there a mitzvah to use philosophy to inquire into the nature of God and the world vis-a-vis what the Torah has to say on these topics?)

2- Did any Rishon feel that philosophical inquiry could produce something that the Torah does not?

3- Did any Rishon fundamentally base their knowledge of God or Torah idea's on the conclusions drawn from their philosophical inquiries?

4- Did any Rishon indicate or explicitly state that their philosophical inquiries took precedence over a straightforward understanding of the Torah (such that the Torah would have to fit whatever the conclusions of their inquiries were)?

(I understand that some of these questions are interrelated, but I split them up anyway because I feel it makes the question/s easier to think about.)