In this paper, we report a number of atypical features of superconductivity, weak ferromagnetism, and quantum transport observed at low temperatures at bicrystalline interfaces of the first predicted and experimentally realized three-dimensional topological insulator (3D TI) Bi1xSbx (0 ≤ x ≤ 0.2). Pure bicrystals and bicrystals slightly doped (≤0.01 at %) with Te (donor) and Sn (acceptor) impurities are used to fully satisfy the conditions of manifestation of transport quantum oscillations. These 3D TI interfaces exhibit fascinating quantum topological properties, which require extensive basic and applied research.