A while ago, I recived about 5 points for no reason, on other occasions I got about 10. Do the moderators on this site sometimes do that because they think the members are good contributors and thus give them more points as a kind of reward?

Thanks for your time.

Nope, we don't give free points, though I might give more points to someone who has sent a very good report.

When you see extra points in certain increments, it most likely means that somebody approved an edit of an old review as though it were a brand new review.

I can usually tell an edited review right off the bat because they seem to queue into the very top of the list for me, but this is apparently not the case for some of the other mods.

No, this is the case. If points were awarded, it's because the mod didn't pay attention and awarded extra points instead of using the drop down.

I have received points for sending a report - at first I thought I had received them in error, but remembered some information I had submitted days prior

Most valid reports will net you 1 point (poor ones net you nothing, and very poor ones may actually result in point loss) apiece, though I personally don't award multiple points for multiple reports when I think they could've easily been made into a single report. If a chunk of the report queue is handled all at once, you might suddenly find yourself with a dozen new points, or so.