Can black mold cause telogen effluvium in every person in home same time?

You should be examined by a dermatologist who is well versed in allergy diagnoses and treatment. Do not try to handle this situation without expert medical care. If necessary consult specialists at the closest medical university as they may have studies revolving around fungal mold and its consequences. 

This is not typically associated with hair loss. That would be very very unusual. Not so say that it can't but that is very unusual. The exception might be an individual who is seriously immunocompromised with widespead infection. Infection with Stachybotrys chartarum or Aspergillus niger  would be theoretically possible to cause a telogen effluvium if one was very unwell with respiratory symptoms, fever and a widespread systemic inflammatory response. Even such a situation would be unlikely to have a long term effect on stem cell populations. All in all it is extremely unlikely that black molds cause hair loss.To confirm whether it is for your family a full examination of everyonr is needed along with an up close exam. A hair collection, trichogram, or biopsy could prove useful. Other tests might too including various blood tests.

Black mold in the household can produce hair loss. You must rid the household of the black mold