We started a multi-scale analysis of G202.3+2.5, an intertwined filamentary region of Monoceros OB1. In Paper I, we examined the distributions of dense cores and protostars and found enhanced star formation (SF) activity in the junction region of the filaments. In this second paper, we aim to unveil the connections between the core and filament evolutions, and between the filament dynamics and the global evolution of the cloud. We characterise the gas dynamics and energy balance using Herschel and WISE observations and molecular tracers observed with the IRAM 30m and TRAO 14m telescopes. The velocity field of the cloud is examined and velocity-coherent structures are put in perspective with the cloud environment. Two main velocity components (VCs) are revealed, well separated in the north and merged around the location of intense N2H+ emission where Paper I found the peak of SF activity. The relative position of the two VCs along the sightline, and the velocity gradient in N2H+ emission imply that the VCs have been undergoing collision for ~10^5 yrs. The dense gas where N2H+ is detected is interpreted as the compressed region between the two filaments, which corresponds to a high mass inflow rate of ~1e-3 Msun/yr and possibly leads to an increase in its SF efficiency. We identify a protostar in the junction region that possibly powers two crossed intermittent outflows. We show that the HII region around the nearby cluster NCG 2264 is still expanding and its role in the collision is examined. However, we cannot rule out the idea that the collision arises mostly from the global collapse of the cloud. The (sub-)filament-scale observables examined in this paper reveal a collision between G202.3+2.5 sub-structures and its probable role in feeding the cores in the junction region. One must now characterise the cloud morphology, its fragmentation, and magnetic field, all at high resolution.
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