margin between plot region and axes

My question: is there a way to add axes the usual way (as tried for the
first graphic), but to erase the margin, so that the axes start at point
(0/0) in my case.

Not really sure if this is what you ask, but maybe you should call
your first plot() with xaxs="i" and yaxs="i". It reduces the default
4% increase on data range on both axis.