Sounds awful what you've gone through, if you've been able to send in medical evidence hopefully this will give you leeway in resolving the issue with them.
The overpayment from what I can work out is likely that if you withdrew before the end date, a portion of your instalments including childcare you won't be entitled to. It may be that you didn't finalise all the childcare forms at the time, so they can't assume you used the money on childcare without them. And it's in the Ts & Cs to keep your address up to date (but I agree, have they never heard of email?)
Perhaps you can call the banks you may have used, they can provide duplicate statements (but may charge for it). Worth checking if your provider is still active, if not perhaps at least you can show the date they ceased trading?
Remember if you're doing some secondary subjects there are bursaries available. And being part way through a PGCE (primary) I swear, make suuuuure you want to be a teacher, because it is an awful course in terms of learning curve and workload. I may be extreme as I had an awful mentor, but during placement I was up at 6 and finishing lesson plans at 12-1am. Happy for lockdown as I have NO idea how I would have managed 10000 words plus another placement.
Keep on top of the work, if you ever have free time do something then and there, never assume you'll have time to do it later. That being said the kids can be lush, but really, from what I've seen in schools, like some of my teacher friends have warned me from the start, is it really worth the stress?
But others on my course have loved it, like I say I was really unlucky.
Don't want to sound too miserable, but there was an element of 'I can get funding for this' that went into my decision, maybe that was my mistake :-) I'm having a rethink on final term in September instead.
I really hope CFS work something out with you!