In this paper, the dimensionless n-component Hirota (alias the n-Hirota) equation is investigated, which describes the wave propagations of n ultrashort optical fields in a fiber. Starting from the modified Darboux transform and its Lax pair with initial non-zero plane-wave conditions, we find the novel multi-parametric families of rational vector rogue wave (RW) solutions for the n-Hirota equation. Furthermore, some weak and strong interactions of rational vector RWs are exhibited for the n-Hirota equation with n=2,3,4,5,6 in detail. In particular, we also deduce the rational vector W-shaped dark and bright solitons of the n-component complex mKdV equation, whose representative wave structures are illustrated for n=2,3,4,5. Finally, the effect of a small non-integrable deformation of the 3-Hirota equation is explored numerically on the excitation of vector RWs in terms of the Fourier spectral method. These obtained rational vector RW and W-shaped soliton solutions will be useful to further explore the related nonlinear wave phenomena in the sense of multi-component physical systems with non-zero backgrounds.