On the Kabblah thing - it's a Jewish mysticism religion.
Ayu has never identified with a specific religion, however it can be thought that she follows Shinto as the vast majority of Japanese follow the its traditions - even if they formally identify as atheists.
I think the red string might be linked to the way people tie red strings to help them remember things - you see it in anime shows a lot where characters tie strings for memories. She might have worn it for remembering 10 years of work? It would be nice to think so but I don't think we'll ever know
I dunno about the Shuya thing, it sure seems like they've got something above a professional relationship!