Regarding your two questions, some terms you could look up are: Courant number, von Neumann stability analysis, Kolmogorov length and time scales
With respect to 2, the standard industry practice is a mesh convergence study and comparing your solver's output to experimental data. Sadly, especially with Reynolds-averaged Navier Stokes, there is no guarantee you'll get a physically correct solution.
Yeah, I know but still had no time to dive into the theory enough to get a correct intuition of how it works on why there's no guarantee for a physically correct solution... Fortunately, my colleagues are the professors in my university who teach these, so I'll find an answer :-)
With respect to 2, the standard industry practice is a mesh convergence study and comparing your solver's output to experimental data. Sadly, especially with Reynolds-averaged Navier Stokes, there is no guarantee you'll get a physically correct solution.