I love this forum, but I hate having to come back to this section because my fish have problems :C Also, I have included pictures that were taken today. Sorry about the giant size.
I recently posted about my delta tail, Haru. He's still in quarantine but he has begun to eat again BUT, his tail seems like it's not healing, nor does it seem to be getting worse. AND I am seeing what looks like fungus on his back. Haru for some reason won't touch the blood worms I give to him, is still acting lethargic, and stays at the bottom of his tank for long periods of time. I have been doing 100% water changes every other day for him.

Here's haru, you can't see the fungus on him but I noticed it literally 3 minutes ago.
One of my original bettas (my second delta tail) died for an unknown reason, but he was much healthier than Haru. I am speculating that something happened with him and a spider because when I was cleaning out the gravel in his section a dead spider was kinda just..lying there. /shudders/ I have replaced him with Tapioca. Who I think will grow a bit more (he's actually pretty small).

He was labeled as a halfmoon, but I'm not sure what he is. There are a few folds in his tails that make me think he's a rose tail, but that could just be a defect in him. Also, some parts of his dorsal fin are extremely thin and are practically see through, should I be concerned about this?
My MAIN problem today, is my double tail, Natsui. Yesterday I was cleaning out their tank, replacing gravel with sand, adding in silk plants in exchange for their old plastic ones, and putting in moss balls and some java fern. Today, I woke up to see that he has made a decent sized bubble nest and he has some small damage on his fins on the tip of his top most caudal fin. I am relatively certain that he was nipping at his tail due to stress (probably when he was in a little cup when I was cleaning everything :C). I add in some aquarium salt and leave for about two hours. I come home to see that the top of his caudal tail and the bottom of his dorsal tail are extremely frayed and ripped.

You can see part of it here.
My main concern is that the edges of the damage have turned red. Is this an infection or is it just blood due to the damage? Also, I might be a bit paranoid, but what can I do to make him stop biting his tail? I hope he'll stop once he's settled down a bit more, but if he doesn't..?
I love my bettas, so thank you in advance for helping me.
tl;dr Haru still having problems, seems like some fungus is growing on him. Natsui is biting his tail, may be infected?