We investigate velocity variations inside and surrounding a gravity-driven drop impacting on and moving through a confining orifice, wherein the effects of edge geometry (round vs sharp edged) and surface wettability (hydrophobic vs hydrophilic) of the orifice are considered. Using refractive-index matching and time-resolved particle image velocimetry, we quantify the redistribution of energy in the drop and the surrounding fluid during the drop's impact and motion through a round-edged orifice. The measurements show the importance of (a) the drop kinetic energy transferred to and dissipated within the surrounding liquid and (b) the drop kinetic energy due to internal deformation and rotation during impact and passage through the orifice. While a rounded orifice edge prevents contact between the drop and orifice surface, a sharp edge promotes contact immediately upon impact, changing the near-surface flow field as well as the drop passage dynamics. For a sharp-edged hydrophobic orifice, the contact lines remain localized near the orifice edge, but slipping and pinning strongly affect the drop propagation and outcome. For a sharp-edged hydrophilic orifice, on the other hand, the contact lines propagate away from the orifice edge and their motion is coupled with the global velocity fields in the drop and the surrounding fluid. By examining the contact line propagation over a hydrophilic orifice surface with minimal drop penetration, we characterize two stages of drop spreading that exhibit a power-law dependence with variable exponent. In the first stage, the contact line propagates under the influence of impact inertia and gravity. In the second stage, inertial influence subsides and the contact line propagates mainly due to wettability.