There are halachic restrictions on a shoita (intellectual handicap) and a deaf person.
As for intellectual handicaps, it depends on how functional they are. Obviously, someone who is incapable of leading the davening or receiving aliyos should not do so.
As for deafness, there are, to my knowledge, no halachic disabilities (vis-a-vis davening) on deaf people that should exclude them for shul activities. There *are* exclusions on deaf-mutes (a mute person, deaf or not, should obviously not lead the davening), but not on people who are only deaf.
There is also some literature that even deaf-mutes today are not the equivalent of deaf-mutes in earlier generations since they can now be educated.
The Wolf