Parallel continuum robots (PCRs) combine the compactness, simplicity, and compliance of continuum robots with the precision and strength of rigid-link parallel robots. In this paper, we provide a generalized Cosserat-rod-based kinetostatic model framework that accommodates various joint types and problem formulations (e.g., forward and inverse kinematics under loads, and deflection-based and actuation-based force sensing) useful for simulation and control. Linearization of this general model provides the manipulator Jacobian, end-effector compliance, input stiffness, and wrench reflectivity matrices, which allow us to examine the effect of design parameters on dexterity, force application, and force-sensing ability. Using ellipsoids based on the matrices, we provide a set of design simulations and graphically depict the relationships between pose, actuation, and forces. We further provide a nondimensional analysis of the compliance of PCRs. Finally, we experimentally demonstrate and validate actuation-based force sensing on a prototype six-degree-of-freedom PCR, demonstrating 3-D force sensing with a median magnitude and a directional error of 0.23 N (8% of actual load) and 12°, respectively.