Reduced-order models (ROMs) are a critical tool for sensitivity analysis, parameter inference, and uncertainty quantification where high-fidelity models would be computationally intractable. Galerkin POD-ROMs are one particular class of ROMs which project high-fidelity model equations onto a set of model solutions to construct ROMs retaining original model parameters and physics, enabling accurate sensitivity analysis, parameter inference, and uncertainty quantification. However, major limitations of POD-ROMs are inability to quantify boundary conditions, identifying new high-fidelity solutions to improve the POD-ROM, and efficiently updating POD modes with new high-fidelity solutions. To solve these limitations, we extend the use of boundary penalties to quantify perturbed boundary values in a POD-ROM of an incompressible Navier-Stokes flow. Next, we derive an approach for determining optimal penalty strengths, bound the error of local sensitivity approximation, and test these advances on an adiabatic tank problem. Finally we propose a sensitivity-based error estimator on which to apply greedy sampling and an iterative mode updating approach using randomized SVD and test these advances on the adiabatic tank problem.