As you can see for yourself, there's an awful lot of detail in this set of problems. It would help me, and perhaps help you, if you were to sort out what you understand already and what you need help with.
(a) asymptotes (vertical and horiz.):
(1) the vertical asymptote(s) are in the form x = a, where x is a root of the denominator of the given function. that denom. is bx^2 + h. We cannot divide by zero, so we play devil's advocate and let bx^2 = h = 0 anyway. Solving that for x (2 values) gives you the equations of the vertical asymptotes.
(2) the horiz asy has the form y=d. d is the limit of the entire function as x grows large without bounds. Note that when this happens, h and k can be neglected. Thus, y = (a/b) is your horiz. asy.
Again, please identify what you understand here and where you need help. I will try to return to this question and help you further then.