I think your question is a good one in light of the more recent publications and discoveries/understanding of what is referred to as the GUT/BRAIN axis of functioning.
is an actual up and coming discipline with professional societies and journals that have been in existence for years though it is not one of the MAINSTREAM considerations by either NEUROLOGISTS or GASTROENTEROLOGISTS in patients such as your daughter.
Therefore, to answer your question" could all or any of this be related to her GUT, intestinal tract?".
I think the answer is a firm MAYBE and probably the easiest place to start investigating a question like that would be a find a SPECIALIST in that area since there are specific approaches and testing protocols that are in place which neither neurologists nor gastroenterologists are necessarily very familiar with since their interests and expertise lie strictly in one discipline or the other.
I would check out the American Neurogastroenterology and Motility Society and their web page at: https://motilitysociety.org/ and see if there is a specialist in your area or somewhere you can take your daughter if you feel strongly that this could be contributory.
The fact that her weight is not under a good control and she likely goes through periods of binging/starvation
(or so it sounds), etc. itself suggests that there is something there which if addressed at least could make brain functioning better.
Certainly absorption of her medications for her mental condition would be enhanced. So I think it's something different to look into which just could offer some ways to improve her situation.
Hope I have answered your query. Let me know if I can assist you further.
Dr Dariush Saghafi, Neurologist