How does Gradient Descent treat multiple features?
That's correct.  The derivative of $x_2$ with respect to $x_1$ is 0.
A little context: with words like derivative and slope, you are describing how gradient descent works in one dimension (with only one feature / one value to optimize).  In multiple dimensions (multiple features / multiple variables you are trying to optimize), we use the gradient and update all of the variables in each step.  That said, yes, this is basically equivalent to separately updating each variable in the one-dimensional way that you describe.