Answer:
Alpha radiation is a kinda massive type of radiation, this would mean that alpha radiation is weakly penetrating. Because of this:
a) When we have particles of smoke in the path of the alpha radiation, the smoke will "stop" a big part of the radiation, and when the detector stops detecting the radiation, it will let the alarm go off.
b) The radiation of alpha particles can be harmful, yes, but the smoke detector is shielded (Again, alpha radiation is weakly penetrating, then shielding the smoke detector is an easy task), this means that the radiation can not get out of the smoke detector, then it is not a problem for the people living near it.