Is it permissible for the tenant to house his parents and brother in the rented apartment for a long period (3-9 months), knowing that he originally informed the landlord that it was for two people only, or is the landlord's permission required?

The tenant may utilize the leased property as they wish, provided they do not cause it any damage. They are not required to seek the landlord's permission for this. Consequently, there is no objection to the parents and brother residing in the rented apartment without needing to seek the owner's permission.