They will not need to know about your diagnosis, per se, they need to know about your hardships and how they impact your experience. So if you say you have a pinched nerve, for example, it's not something they can make a determination with. If you say the pinched nerve makes it impossible to stand for more than Thiru minutes but you can sit, they may determine a wheelchair is an appropriate accommodation. I don't know all the one and outs of how they determine what, but they do it based on the symptoms, not the diagnosis. same for the anxiety.
As for the guest services experience, is really pleasant and short. You show up with your whole party and request DAS. Answer any questions they ask. If you're approved, they'll take your picture with the iPad, and add everyone in your party to your DAS (again, they have to be physically there). When you use your DAS you just need to tap in first, then the CM at the ride will push their button, and then your family can tap in behind you.
We haven't used the online DAS yet so I can't speak to that.