The momentum transfer vector is defined as the difference between the incident vector and the scattered vector. In the case of coherent light scattering, the momentum transfer vectors can be constructed in the Ewald's sphere (or in the reciprocal space). Thus, the magnitude of the momentum transfer vector somehow relates the length scale of the scatterer. Why is that? Also, what does it mean by "the scattering amplitude", how is it related to momentum transfer vector magnitude? I'm so confused.
You may visualize atom as nucleus surrounded by an electron cloud. Now imagine the incident plane wave is scattered by two parts of the electron cloud (front and back). If rays are going in forward direction (near 0 angle, low momentum transfer vector) then the path difference between two beams is less and you will have good constructive interference i.e. larger scattering amplitude. Whereas as you go towards larger angles (higher momentum transfer vectors) the path difference between the scattered rays increases and lesser rays are likely to have constructive interference hence the scattering amplitude goes down. Moreover as the number of electrons surrounding an atom increases the overall scattering amplitude increases. I hope the above explanation would help you.
You may try the book "Elements of x ray diffraction" by B. D. Cullity Chapter 3 and 4 will help you in understanding basic processes.