I'll have to try and replicate your editor positioning problem. In general the equation editor should appear as a popup window and paste text to the current cursor position. We have to do some tricks to make this work across all browsers.
As for dy/dx, this is really just a fraction, i.e.
\frac{dy}{dx}
gives
d^2y/dx^2 is only fractionally more complex
\frac{d^2y}{dx^2}
which gives,
Most of the commands on the current equation editor are focussed on helping us find the relevant latex command (i.e. \frac in the previous examples). What you're asking for is taking this one step further and including some preset equation forms. Another perhaps should be