can $\frac{1}{H(z)}$ be causal and stable? if we have linear phase FIR filter $H(z)$ which is causal and stable 
can $\frac{1}{H(z)}$ be causal and stable ?

can it be causal without been stable ?
For 1/H(z) to be causal, it must not have more zeroes than poles. Therefore, H(z) must not have more poles than zeroes.

If H(z) has linear phase, then it must have zeroes either in the unitary circle or simultaneously inside and outside of it. Therefore, 1/H(z) can't be stable if H(z) has linear phase.