The main goal of this work is to develop a data-driven Reduced Order Model (ROM) from high-fidelity simulation result data of a Full Order Model (FOM), in order to predict at lower computational cost the time evolution of solutions of Fluid-Structure Interaction (FSI) problems. For some FSI applications, the elastic solid FOM (with neglected inertia) can take far more computational time than the fluid one. In this context, for the sake of performance, one could only derive a data-driven ROM for the structure and try to achieve a partitioned FOM fluid solver coupled with a solid ROM. In this paper, we evaluate the partitioned ROM-FOM coupling on study cases with strong coupling: an incompressible 2D wake flow over a cylinder facing an elastic solid with two flaps, and a 3D model of a flexible artery[1]. We evaluate the accuracy and performance of the proposed ROM-FOM strategy on these cases while investigating the effects of the model's hyperparameters, especially with the presence of complex/chaotic dynamics. In addition, we show the effect of the structural ROM on decreasing the coupling rate of convergence. To mitigate these issue, and we present an additional data-driven approach, that further accelerates convergence, while implemented non-intrusively within the framework of partitioned FSI coupling and Quasi-Newton acceleration techniques[2]. We demonstrate on the considered test cases a high prediction accuracy and significant speedup achievements using our proposed strategy. [1] L. Formaggia, J.F. Gerbeau, F. Nobile, A. Quarteroni, On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels, CMAME, 561-582, Vol. 191, 2001. [2] Delaissé, N., Demeester, T., Haelterman, R. et al. Quasi-Newton Methods for Partitioned Simulation of Fluid–Structure Interaction Reviewed in the Generalized Broyden Framework. Arch Computat Methods Eng} Vol. 30, 3271–3300, 2023.