Generating mocks for future sky surveys requires large volumes and high resolutions, which is computationally expensive even for fast simulations. In this work we try to develop numerical schemes to calibrate various halo and matter statistics in fast low resolution simulations compared to high resolution N-body and hydrodynamic simulations. For the halos, we improve the initial condition resolution and develop a halo finder "relaxed-FoF", where we allow different linking lengths for different halo mass and velocity dispersions. We show that our relaxed-FoF halo finder improves the common statistics, such as halo bias, halo mass function, halo auto power spectrum, cross correlation coefficient with the reference halo catalog, and halo-matter cross power spectrum. We also calibrate small-scale velocities of small halos to improve the power spectrum in redshift space. For the matter statistics, we incorporate the potential gradient descent (PGD) method into fast simulations to improve the matter distribution at nonlinear scales. By building a lightcone output, we show that the PGD method significantly improves the weak lensing convergence tomographic power spectrum. With these improvements FastPM is comparable to the high resolution full N-body simulation of the same mass resolution, with two orders of magnitude fewer time steps. These techniques can be used to improve the halo and matter statistics of FastPM simulations for mock catalogs of future surveys such as DESI and LSST.