Screenshot right, that a nice feature.
The insert problem. Then put a writing on the chart that it is inactive and if you choose "move" send a brief "insert" and then set "move".
Then by default you'd only have one point to work with, whereas people might want more. I've made a few changes though that might simplify things a bit
1) bigger chart, so easier to click where you want
2) the insert/move/delete/curve dropdown is now radio checkboxes, so you can change modes with one click
3) when in insert, if you try to insert on the same x-coordinate as an existing point, it will instead move that point (it used to ignore this, which is probably why it seemed unresponsive to you)