> I've seen somewhere the advice that if your crampons are vertical points, you should sharpen them like you would sharpen the pick of an ice tool.
Yes, if you try it you'll find its the only obvious way to do it.
> So, should you remove the first tooth on your vertical monopoint crampons?
I can't think any reason why that would be a good idea. In comparison to tool picks, the sharpness of crampons seems to make little difference within reason. I quite regular sharpen my picks, perhaps every second day of ice climbing through the winter if they touch rock. But I sharpen my crampon front points once a season at most.