(c) Is hydrostatic balance more or less likely in rotating flow?

Hydrostatic balance states $\partial_z\phi\sim b$ and neglects vertical acceleration $\partial_t w$ compared to vertical pressure gradient. For non-rotating flows, typical vertical acceleration scales like $U^2/L$ while the pressure gradient scales like $\Phi/H$. Using $\Phi\sim U^2$ for non-rotating flows one finds that hydrostatic balance can break down when vertical scales are comparable to horizontal scales.

In a rapidly rotating flow, however, geostrophic scaling gives $\Phi\sim f U L$, which can be much larger than $U^2$ when $Ro\ll1$. Vertical acceleration is associated with ageostrophic motions and is smaller by factors of $Ro$. Thus the ratio of vertical acceleration to pressure gradient is reduced in rapidly rotating flow, making hydrostatic balance more likely to hold. Intuitively: rotation tends to suppress vertical motion (via columnar Taylor–Proudman tendencies and geostrophic nondivergence) and thus reduces vertical acceleration relative to pressure gradients, favoring hydrostatic balance. Therefore hydrostatic balance is more likely to hold in rapidly rotating flows than in non-rotating flows, all else being equal.