Thule comes from a Greek cartographer, Pytheas. Thule was supposed to be an island to the north of Britain, but nobody knows what he referred to or if whatever place he referred to even was real. Some people, especially 19th century Scandinavian nationalists, associate Thule with Scandinavia.
Unlikely. Thule was supposed to exist in 330 BC, long after Doggerland had disappeared. There are many other candidates which would make more sense and fit better with his descriptions, including Norway.