In this thesis, we discuss several topics related to the field of Ricci flow. Our first topicconcerns the second curvature operator and its behavior under the Ricci flow. We produce an explicit description of the eigenvalues of this operator in dimension 3, and using this, we show that a large class of positivity conditions are preserved by the Ricci flow. As an application of our description, we attain a refined classification result for manifolds satisfying such curvature conditions. Our second topic pertains to Minkowski estimates for the singular set of an F-limit of non-collapsed closed Kähler Ricci flows. We prove an ϵ-regularity theorem for non-collapsed Ricci flows that are Kähler or of real dimension 4. Using this, we show that, in these cases, a certain finite energy condition is sufficient to gain sharp volume bounds for the singular set in the limit. As an application, we reproduce some known estimates for singularity models of the Fano Kähler Ricci flow due to Chen and Wang. Our techniques involve introducing a new notion of uniform convergence of functions within a correspondence for a sequence of F-converging Ricci flows, which is of independent interest.