As far as I know all spoiler races are jump capable.
Not all of their ships are, however, and I think Precursor are the one race with the fewest jump capable ships. This is solely based on my personal experience, but I'd say the Swarm has the most jump capable ships (all but the FACs are jump capable), followed by the Invaders, whom employ their own grav survey ships and a braod range of jump capable ships. I think seeing Precursors jump is quite rare, but very well possible.
To answer your question about swarm sizes, they come in three larger sizes and various FACs. Their matriarchs range 200kt, motherships 60kt, some 6kt class and their FACs all at 800 tons with 10kkm/s speed, as far as my observations go. These FACs are then either worker drones or warriors.