In case of FIR filter design, is the following relation always applicable or there are other relations/formulas also?
If window length is denoted by $M$ ,then filter order will be $M-1$
Yes. The number of taps or coefficients in a FIR filter (or window length as you call it) tell the order of the filter. A more general way to see it, to avoid confusions, is to think of the order as the largest delay in the filter. For example, consider the following naive reverb:
$$y[n] = a x[n] + (1 - a) x[n-D]$$
Even though there are only two (visible) coefficients, the order of the filter is $D$ because it’s the largest delay. The window length is $D+1$ but all the middle coefficients are $0$, hence not visible.