Unfortunately, no. The EOS 100 M has an EF-M bayonet mount, but the lens has an EF-S mount. However, Canon also offers an adapter with which EF-S and EF lenses can be used.
15 pieces of the non-import version are in the Black Friday promotion and can therefore be offered at a very attractive price. As soon as the 15 pieces are gone, the "old" price will be displayed again.
Canon EF-S 55-250mm f/4-5.6 IS STM
Hello. Yes, it fits. All lenses with EF and EF-S mount fit. Note that the focal length is not 55-250mm due to the APS-C format sensor, but 88x400mm (crop factor).
Hope this helps