Assuming you can avoid rope abrasion, do swings like this damage climbing ropes? Swing goes straight into a pendulum with no/limited
I can't see it doing any special damage to the rope that wouldn't occur through climbing. I would make regular inspections of the rope and retire/replace equipment when necessary. The fall factors involved are well within the 1.7 tested by the UIAA but it might be worth contacting the manufacturer of the rope to see if they have any information about how the ropes perform in the pendulum type fall rather than a straight one.
The figure eights get very tight at the anchor. I've heard people say you should loosen them, retie them, or cut them away after several
jumps. Any truth to this?
If you can't untie them then I guess you'll have to cut them. If this is happening regularly than maybe you can prevent it by undoing and retying so they aren't getting repeatedly tightened with each jump. I'd say if you can untie them then you don't need to redo them, your just adding more opportunities to make a mistake. If you find that the rope is becoming deformed or the sheaf is getting damaged then that part of the rope is no longer safe and should be cut out.
We set up a prussic chord at the anchor. It attached just below the
figure eight knot that secured the jump line. This kept the weight of
the jump partially off the knots. Are there risks associated with
this, eg. can prussics weaken a system like this, or cut the rope?**
A figure of 8 is a very efficient knot, retaining about 80% of the ropes strength. I don't know of any figures that show the efficiency of a adding a prussic to a rope but I doubt it is making the system stronger. It is also just another way to add a point of wear to the rope. Lastly what are the prussics attached to? surely loading the weak prussics instead of the strong rope is not desirable. I would personally avoid doing this.
We also jumped onto a prussic (primary), with an atc below, with overhand knot below that. We clipped the bite from the overhand knot
to our belay loop. We did this because we jumped with a backpack and
had to rapel to the ground after the swing completed. Slightly
clustered, but we wanted to easily rapel after the jump was completed.
Any feedback on this setup?
Again is the prussic on your harness directly loaded in the fall? You want to give yourself the widest safety margin you can so that would look more like clipping into a figure of eight with a carabiner designed to avoid cross loading. Prussics and ATC on the harness ready to use once you come to a stop.
Caveat: This isn't the way to swing on a rope more a critique of your current set-up from a climbing perspective.