No, you can only use it in the AW it is for. So, you can put it in another player's GA for 15AWKP, or into your GA for 10AWKP. You couldn't use it for 10AWKP in your Monatsery/Sanctuary, for instance.or you can use it in any aw of yours for 10kp.
I have a 5, 10, 15, 30, 45, 60, 75 and 100. I do not differentiate between runs shard swaps and regular threads, use the 15, 30, 45 or 75 if you want to use rune shards. Keep a weather eye on stocks, and on your outbound vs inbound KPs, because there is a hard cap.Since the shards have to match the AW, I don't see how just one thread would be workable. Am I just being dense?