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Difference between Fundamental , Essential and Homography matrices

I have two images which are taken from different positions. The 2nd camera is located to the right,up and backward with respect to 1st camera. So I think there is a perpective transformation between the two and not just affine transform since camera are at relatively different depths (am I right ??) I have few corresponding points between the two images. I think of using these corresponding points to determine the transformation of each pixel point from 1st to 2nd image.

I am confused by the functions findFundamentalMat and findHomography.... both return 3x3 matrix, what is the difference between the two ??

Is there any condition required/prerequisite to use them (when to use them)??

Which one to use to transform points from 1st image to 2nd image?? In the 3x3 matrices which the functions return, do they include the rotation and translation between the two image frames??

From wikipedia, came to kmnow that Fundamental matrix is relation between corresponding image points. In an SO answer here, it is said Essential Matrix E is required to get corresponding points... but I do not have the internal Camera matrix to calculate E.....I just have the two images.

How should I proceed to determine the corresponding point? Awaiting for suggestions.. Thank you