Clare I had the same problem, instead of adding back I clicked their name and added that way, I doubt its a fix but I wanted them to know I was happy to add them.
I don't know if this is related, but I think it might be because it just stays loading as well after the test - the wardrobe. I don't know if it was happening before the test ended, but I went to change my outfit and it won't load now.
Yes I had the same problem and I used the same workaround as Faereluth. Or I clicked on their name from the invite and added to friends from their profile.