Gluten intolerance is a real thing but I don't think that necessarily means that your gut flora is damaged or whatever. Plenty of people are lactose intolerant, and their gut flora is fine, they're just lactose intolerant.

I don't think you could solve gluten intolerance but just improving your gut microbiome, so they're probably not related.

Why not? A fecal transplant seems to work for C. difficile sufferers.