We present an analysis of the individual observations of a deep XMM-Newton survey of the Local Group spiral galaxy M 33. We detected a total of 350 sources with fluxes (in the 0.2-4.5 keV energy band) in the range 6.7 × 10 −16 −1.5 × 10 −11 erg s −1 . This comprehensive study considers flux variability, spectral characteristics, and classification of the detected objects. Thirty-nine objects in our catalogue are new sources, while 311 were already detected in a previous analysis of most of the same data using combined images. We present improved positions of these sources and the X-ray parameters of each source in each individual observation that covers the source. We then used these parameters to systematically search for flux variability on time scales of hours to months or years. The long-term light-curves were generated for the 61 sources showing a significant variability of the (0.2-4.5) keV flux, by a factor of 1.2 to 144. The detected variability was then used to classify 8 new X-ray binary candidates in M 33. Together with the hardness ratio method and cross-correlation with optical, infrared, and radio data, we also classify or confirm previous classification of 25 supernova remnants and candidates, 2 X-ray binaries, and 11 super-soft source candidates (7 of which are new SSS candidates). In addition, we classify 13 active galactic nuclei and background galaxies, 6 stars, and 23 foreground star candidates in the direction of M 33. Further 206 objects are classified as "hard", approximately half of which are sources intrinsic to M 33. The relative contribution of the classified XRB and SSS in M 33 is now comparable to M 31. The luminosity distribution of SNRs in both spiral galaxies is almost the same, although the number of the detected SNRs in M 33 remains much higher.