In its many embodiments, the present invention provides certain C5-C6-oxacyclic fused iminothiadiazine dioxide compounds bearing an ether linker, including compounds Formula (I): or a tautomer thereof, and pharmaceutically acceptable salts of said compounds and said tautomers, wherein RN, R1, R2, RA, ring A, ring C, and m are as defined herein. The novel compounds of the invention are useful as BACE inhibitors and/or for the treatment and prevention of various pathologies related thereto. Pharmaceutical compositions comprising one or more such compounds (alone and in combination with one or more other active agents), and methods for their preparation and use, including for the possible treatment of Alzheimer's disease, are also disclosed.