Star clusters are crucial for understanding how stars evolve. Their colour- magnitude diagrams show the effects of stellar evolution of approximately coeval objects with the same chemical composition. Furthermore, the determination of their astrophysical parameters (age, distance, colour excess and metallicity) together with their spatial distribution provides information about the structure and the evolution of the Galaxy itself. Using data from the Gaia DR3 and 2MASS catalogues, we develop methodologies for characterizing open clusters. Precise membership lists, mean astrometric parameters and radii are obtained. Using photometric data from both data sources, we carried out new age calibrations that rely on morphological indices based on colour ({DELTA}B-R) and magnitude ({DELTA}G) differences between the red clump and the turnoff for a sample of 34 open clusters with ages covering the interval 8.3<log[t(yr)]<9.9. A set of age calibration functions based on Gaia morphological age indices are determined for the first time. We demonstrate their accuracy, obtaining a mean residual of 0.06 dex in log[t(yr)]. Our results also show that stellar evolution models tend to predict the difference {DELTA}G. However, they typically overestimate the difference {DELTA}BR for objects younger than log[t(yr)]=8.8.