Is it possible to transfer Minecraft worlds created on the Nook to a copy of Minecraft on the iPad Mini? If so, how?
No, it is not. The two devices run different operating systems which make the two world saves incompatible. The only way would to somehow access the hard-drive from the Nook, find the world saves, translate them into something that iOS can read, and hope for the best. However, that process would both void your warranty, and be virtually impossible.