A lot of it really depends on what foods they do like. For example, my DS (milk, egg, nut allergic) is a big eat meater, so we target places like Le Cellier, Whispering Canyon Cafe, Cosmis Rays, Flame Tree BBQ, and Liberty Tree Tavern.
With that many allergies and this being a first trip, I would avoid any non-Disney owned restaurants. I don't have a complete list, but most in the World Showcase (Le Cellier and Biergarten are exceptions), DTD, and Kouzinnas come to mind. Chef Mickey's breakfast is one we do every trip. I've never been for lunch or dinner, so I don't know what they serve FA customers, but for breakfast they should be able to get Mickey Waffles, some safe fruits, sausage, and bacon.
I recently posted my DS's meals for a recent trip. He doesn't have as many allergies as they do, but he has the big ones and I think many of his meals would have worked for your friend.
I see they don't have a dairy allergy, so they should be able to get real butter. Tell her to be sure she never gets offered the "allergy" butter as it is Earth Balance and likely contains peas. I just see this as a possible point where a Chef could slip up.
Bread is going to be an issue. They probably won't be able to have any rolls/bread with meals. The QS buns may be safe if they're not dairy allergic.