In ABAQUS/Explicit, the total mass of the model is printed in the status (.sta) file - look under 'Model Information'.
In ABAQUS/Standard, the mass is printed to the .dat file - search for 'mass' within the .dat file.
As for stiffness, it would depend on what you are trying to achieve. A would expect a model to have different stiffness in different directions, so you would have to consider how you set up your boundary conditions and loads to achieve this. Just asking for the 'stiffness of the whole model' is a bit too vague.
Regards
Martin