  Constraints on dark matter halo masses from weak gravitational lensing can be
improved significantly by using additional information about the morphology of
their density distribution, leading to tighter cosmological constraints derived
from the halo mass function. This work is the first of two in which we
investigate the accuracy of halo morphology and mass measurements in 2D and 3D.
To this end, we determine several halo physical properties in the MICE-Grand
Challenge dark matter only simulation. We present a public catalogue of these
properties that includes density profiles and shape parameters measured in 2D
and 3D, the halo centre at the peak of the 3D density distribution as well as
the gravitational and kinetic energies and angular momentum vectors. The
density profiles are computed using spherical and ellipsoidal radial bins,
taking into account the halo shapes. We also provide halo concentrations and
masses derived from fits to 2D and 3D density profiles using NFW and Einasto
models for halos with more than $1000$ particles ($\gtrsim 3 \times 10^{13}
h^{-1} M_{\odot}$). We find that the Einasto model provides better fits
compared to NFW, regardless of the halo relaxation state and shape. The mass
and concentration parameters of the 3D density profiles derived from fits to
the 2D profiles are in general biased. Similar biases are obtained when
constraining mass and concentrations using a weak-lensing stacking analysis. We
show that these biases depend on the radial range and density profile model
adopted in the fitting procedure, but not on the halo shape.
