Will this structure emit EM waves when excited by out-of-plane time varying magnetic field?
will the protruding wires emit EM waves?


Yes. But then, there will be EM waves all over such a setup anyway.


  If yes, will the emitted radiation have a frequency of f?


Yes, of course. This is a linear, time-invariant (LTI) system, so it couldn't have any other frequency.


  And will x affect the power of the emitted radiation?


Yes. Look up dipole antenna. The radiation varies in a complex way, depending on how x relates to the frequency (wavelength) and how the inductance and capacitance of the coil resonate with the antenna.