Interpreting how graphs of Cobb-Douglas utility functions. How does MRS vary as we vary $\alpha$?
If $\alpha$ rises, the utility puts more weights to the $x$. Then you must give up more $x$ for one $y$ (for the same utility). Your MRS, for a given $y$, increases in absolute value. Graphically:


If you set $y$ and $x$, the slope is lower for higher $\alpha$ (be careful to only change one thing at a time).

Concerning your "loop" problem, look at the function $1/x$, the first derivative is also a function of $x$, like the 2nd and so on. What matter is the value at one particular x.