For the first
>question, check the documentation for the "units"
>command. It should be mentioned there.
I checked here: LAMMPS Molecular Dynamics Simulator
and it's not mentioned.
Indeed it is not, sorry about that.
https://lammps.sandia.gov/doc/compute_omega_chunk.html calculates omega in units of velocity/distance units. If the omega function in variable is consistent with that (I would assume/hope it is), then for real units that would then be 1/femtosecond, which would be equivalent with rad/fs.