  In this work we keep pushing K2 data to a high photometric precision, close
to that of the Kepler main mission, using a PSF-based, neighbour-subtraction
technique, which also overcome the dilution effects in crowded environments. We
analyse the open cluster M 44 (NGC 2632), observed during the K2 Campaign 5,
and extract light curves of stars imaged on module 14, where most of the
cluster lies. We present two candidate exoplanets hosted by cluster members and
five by field stars. As a by-product of our investigation, we find 1680
eclipsing binaries and variable stars, 1071 of which are new discoveries. Among
them, we report the presence of a heartbeat binary star. Together with this
work, we release to the community a catalogue with the variable stars and the
candidate exoplanets found, as well as all our raw and detrended light curves.
