Resonance frequency of filter independent of resistance?
Is the resonant frequency independent of the resistance?


The natural resonant frequency is independent of the series resistance.


  Why even include it then?


The inductor has series winding resistance so you can't ignore it. If you were doing a more complex analysis of the circuit like trying to find the magnitude of the transfer function (for instance), you need to include it.


  What is the resonance frequency of the filter, \$\dfrac{I_{out}}{I_{in}}\$?


No, that's a transfer function and not the resonant frequency.