I can't answer all of your questions, but one thing first, read some of the blog-posts on - Jack Kruse. He has written some very eyeopening posts on food, leaky gut, hyperthyroid etc etc. Very difficult reads but mind-blowing.
If you still feel hungry after meals I can only suggest for Mollie to add more fat, as in eating coconut oil off a spoon. I do this 3 times daily and I never feel hunger. As for you, I'd up the protein but go a bit more modest on the fat.
About the exercise: don't push yourself until you are better. You both have massive issues to deal with here, your bodies need to heal and repair. Trust me when I say that the urge, desire and need to go hard with the sprints and weights will come as your body is in a better place. It did for me. It was like I woke up one day and just had to lift heavy and run fast. Very odd.
I think 7 weeks might jot be enough time o heal to get to that point where you have soaring energy levels.
I was going to say leaky gut myself. I have it too, but only 2-3 foods I'm allergic to now. I saw a naturopath, as leaky gut is a precursor for autoimmune disease like diabetes type 2. I'm already pre-disposed through genetics, so I am desperate to cure my leaky gut.
I'm on a high dose of wild salmon oil, I take zinc, glucosamine, magnesium and a large dose of probiotics daily. Someone else here suggested bovine colostrum. You should also move lots, like walking daily. I hope this helps, and good luck on your journey to better health.