There are many mistakes in your post

anyway to find the dy/dx differentiate separate first and find dy/dt then dx/dt and then find dy/dx=(dy/dt)/(dx/dt) . verify your post because you may have typed wrongly the parametric equations. anyway if you do corect the calculations you will find the dy/dx.

For the second question something is missing...the curve y=(2x-5)/(x^2-4) has as domain R-{-2,+2} and has 3 branches. The part of the curve which is defined in the domain (-2,+2) has range y biger or equal to 1.... with the lines x=-2 and x=+2 to be the vertical asymptotes .

I don't understand what you want...

For the last question try to find a graph calculator to see the shape of the graph and then try to graph it.