a) sight vs. seeing: Seeing is the act of perceiving by means of the eyes, whereas sight is either what is perceived or the ability to see.
b) movement vs. moving: This is somewhat tricky. As an analogy to a) we could say that a movement is a change in position or pose, while moving is actually changing that or that changing and the way in which it happens (i.e. it can be either a transitive or intransitive verb). What is tricky is that moving is also an adjective, used for something in motion.
c) speed vs. velocity: synonymous. A burst of speed: a sudden increase in speed. Speed is the rate at which movement occurs.
d) Look at, take a look at.
Hope this helps.