"Abdoolhoosen" seems to be an anglicisation of Abdul Hussein, as spelt on one of the Carl Smith cards that references him. The name "Abdoolrahim" is also an anglicisation. A. Abdoolrahim appears on the Jurors List for many years and seems to have worked his way up from clerk to draughtsman to architect. He is credited on the 1903 list of Authorised Architects of Hong Kong and founded his own company, Abdoolrahim & Co., 34 Queen's Road Central, which also employed other architects.
As I am cataloguing the earliest owners of the houses in Broadwood Road, Abdoolrahim seems to have been briefly the owner of "Lyndholme", originally no.19 and then no. 18 Broadwood Road in 1916-17, however Emulji Mogra is given as the actual rate payer and the Mogra family lived there at the time, recorded in the Rate Book as "c/o Abdoolrahim."
I don't know the early history of the Abdoolrahim family in Hong Kong.