Are the home office allowed to take away my passport?
The home office could take away your passport if they established that you'd gained it by deception. For example, a person who naturalized as a British citizen is asked to make a declaration that all the information they give is honest and truthful. If it was subsequently established that you had given incorrect information or false documents to the home office in order to obtain that nationality and passport, then the home office would be within their rights to take that passport away from you.