Zero phase filter and Period of a Signal

Hello, forgive me if this has been asked before

My query is two-fold, not necessarily related.

Suppose I am given an arbitrary periodic signal. I understand how to find the component frequencies via fft(). However, I am unsure how to find the overall frequency/period of the signal. How would I go about this? I know this can be done, say, by inspecting the graph of the signal, but I'm looking for a more "algorithmic" approach.

Secondly, suppose I have a linear-phase FIR filter. I know I can find its roots, create a polynomial and find the magnitude and phase response via freqz(). I also know that if I wanted to make it zero-phase, I would need to time-shift to the left. How do I go about implementing this in matlab, such that I can see an output similar to freqz()? The input arguments of freqz() only use negative indices of a polynomial, where as I need positive as well.

I hope this makes sense.

Regards, A