  [Abridged] Classical novae (CNe) represent the major class of supersoft X-ray
sources (SSSs) in the central region of our neighbouring galaxy M31. We
performed a dedicated monitoring of the M31 central region, aimed to detect SSS
counterparts of CNe, with XMM-Newton and Chandra between Nov and Mar of the
years 2009/10, 2010/11 and 2011/12. In total we detected 24 novae in X-rays.
Seven of these sources were known from previous observations, including the M31
nova with the longest SSS phase, M31N~1996-08b, which was found to fade below
our X-ray detection limit 13.8 yr after outburst. Of the new discoveries
several novae exhibit significant variability in their short-term X-ray light
curves with one object showing a suspected period of about 1.3 h. We studied
the SSS state of the most recent outburst of a recurrent nova which had
previously shown the shortest time ever observed between two outbursts (about 5
yr). The total number of M31 novae with X-ray counterpart was increased to 79
and we subjected this extended catalogue to detailed statistical studies. Four
previously indicated correlations between optical and X-ray parameters could be
confirmed and improved. We found indications that the multi-dimensional
parameter space of nova properties might be dominated by a single physical
parameter. We discuss evidence for a different X-ray behaviour of novae in the
M31 bulge and disk. Exploration of the multi-wavelength parameter space of
optical and X-ray measurements is shown to be a powerful tool for examining
properties of extragalactic nova populations. While there are hints that the
different stellar populations of M31 (bulge vs disk) produce dissimilar nova
outbursts, there is also growing evidence that the overall behaviour of an
average nova might be understood in surprisingly simple terms.
