Compensating for group delay in FIR with symmetrical coefficients
No.

There is no way you can compensate for a  broad-band group delay without violating causality. If you add zeros at the end of your signal, the group delay stays constant and if you add zeros in front of it, the group delay goes up.

At some frequencies it may look that there is no group delay (or phase shift), but that's just an illusion: the phase of the filter at this frequency just happens to be an integer multiple of two pi. If you look at any other frequency, it won't be true any more.