The turtle in question is about ~7" and lives outdoors in our ~45 gal backyard pond. The temperature outdoors has been in the mid-80s recently but in the 90s and 100s before that, so I don't think the water is too cold, although I don't have a thermometer in it. We have a pump/filter that seems to work tolerably well, and we changed about half of the water a couple weeks ago. The pH, alkalinity, and hardness are kinda high.
History:
While home from college on break last April, I was driving with my brother and he spotted a turtle in the middle of our street (we live in the city). The turtle looked somewhat beaten up with white showing from under its shell and a large crack on the left side of its shell. We took it home and put it in a tub of water in our backyard (there was no water in the pond at that point). It apparently didn't like the water, and while we weren't looking climbed out and disappeared.
I found it a couple months later buried in leaves under one of our bushes. The pond now had water in it so I put the turtle in with the goldfish. I assumed the turtle had health problem but would start getting better because:
-It spent months (apparently) not eating, but now has a voracious appetite for turtle pellets and the leaves of my mom's water plant.
-It used to be extremely sluggish, spending all its time sleeping in the bush, but now is extremely active, swimming back and forth floating on the surface, occasionally chasing the goldfish (although it's not eaten any...yet), and spending a couple hours each day sunning itself on a rock. It was very hard getting pictures of it because it would not stay still. I think in the proverbial turtle vs. hare race, this turtle would win without any competition.
The Problem:
I just noticed the crack on the turtle's shell has worsened. In fact, it's not just a crack anymore--a whole chunk of shell is missing. Also, one of the original white spots on the shell is soft, although I never checked it before so maybe it always has been. Is it rot, fungus, calcium deficiency? I think it's safe to say this turtle has not been getting enough veggies. It's eaten all the leaves that it can reach on the water plant, but that's certainly not 50% of its diet. Could that be aggravating the problem? Thanks for your advice.
btw, there is also a small, ~2" RES living in the pond. We moved it there from its <1 gal tank a little before we put the big turtle in and it seems to be fine, at least there's nothing wrong with its shell.
The habitat:
Presumably healthy behavior of fleeing from the camera:
The problem areas:
Front problem:
Back problem:

