The contribution of Coriolis forces to the evolution of system is determined numerically by the Rossby number (Ro) representing the ratio of involved centrifugal to Coriolis accelerations. The smaller Ro, the greater the contribution of Coriolis forces. The recent measurement of Rossby number by the helioseismology of solar interior turned out to be Ro
Yes definitely, the structure of stars must be distorted by the the effect of Coriolis forces, as it arises due to the rotational motion of materials present on the stars. Even Newtons first law describes the effect force.