So you do have a minor misconception there in that first paragraph, time dilation is relative. The slowdown of something falling into a black hole is seen from the perspective of a distant observer, the thing falling in experiences time normally but sees the outside universe running in fast-forward during the fall toward the horizon. Neither is losing energy, the extreme curvature of spacetime stretches out the light moving outward and compresses it in the other direction.

As to whether any particles can catch up to each other beneath the event horizon, our best theories suggest it is indeed possible. The steeply curved spacetime beneath the event horizon should still include valid paths where particles thrown in at an angle will intersect with each other as they spiral in. Velocity is relevant too, something that dives in at 99% the speed of light should be able to catch up to something that was dropped from a relative standstill just above the horizon if the time gap between them is small enough.

Also, space isn't just "the gaps between things", it's dynamic, squashing and stretching in response to gravity and expanding due to dark energy. We have to account for these effects in order to keep the atomic clocks in our GPS satellites synced and the system functional.