Sorry for the late reply. I would usually do habitat selection with the location data. There's some new and in-development autocorrelation-weighted & integrated RSF code in the development version of the package on GitHub (see help('rsf.fit')). It also automates numerical convergence.
The grid displayed when plotting the AKDEs is obtained from the bandwidth matrix in the 'H' slot of the UD object. This is kind of like a covariance matrix for the individual kernels that make up the AKDE. The grid is calculated from the matrix-square-root of this matrix, which is like a matrix of standard deviations. I doubt you need this, though.
For making simpler comparisons with the AKDEs, I personally wouldn't do
anything much more complicated than calculating expectation values with
the distributions, which is easy. If PMF is the exported PMF of the AKDE and R is a raster of covariates, and they are in the same projection with compatible grids, then sum(PMF*R) is the expected value of covariate, E[R], according to that distribution, and VAR[R] is