There is a good reason why the front isn't indexed. As you move the chain up and down the rear cogs, the angle of the chain changes. You can make minor adjustments to the FD to compensate for this. The lever shouldn't move by itself. Tightening it as instructed above should fix that problem. If that doesn't work, try lubing the cable where it goes under the bottom bracket. Another possibility is your cable and housing are old and need to be replaced.