(b) The velocity is the derivative of position with respect to time
(c) The acceleration is the second derivative of position with respect to time
(d) To find local extrema of functions we try to find the stationary points (points where the derivative = 0) and then confirm that they are maxima asserting that the second derivative < 0. Since this function happens to have a single local extreme it is an easy task
(e) This is equivalent to finding the 't' that maximizes the function. You find this while solving (d)
(f) The same as before but now dealing with velocity instead of position.
(g) Same as e
(h) The instant the particle isn't moving => v=0
(i) I hope you know (intuitively) how to find the average velocity of something