Yes! I saw it at the 36 minute mark on the video. That had me curious. I think it was a trick of perspective, it first looked like some huge chunk of debris that the first stage flew past, but after watching it again, it looks like a little chunk of ice that got blown off of by the cold gas thrusters.

Yes, that's it, a few seconds after the 36 minutes mark. I think you're right, and it does look a lot smaller upon rewatching!

Yes! Wait are you talking about the second stage that was in the right/second monitor? I am.

I thought it was weird that the two pieces stayed with the second stage for at least a second or two, which was literally ~five+ kilometers. Perhaps there was an eddy created by the movement of the rocket or some weird space/vacuum effect I'm not well-versed in?

The second stage debris that you are talking about showed up when the stage stopped accelerating. The debris and stage were moving at the same speed, so it's normal that they drifted apart relatively slowly.

If you look back at old launch videos, you can often see big chunks of ice form by the second stage engine vents during coast, only to be blown off by the vibration as the engine is restarted. I assume this is something similar.