Carbon black is produced due to incomplete combustion of heavy petroleum products. It is used in rubber as pigment thats how it gets its black color. (e.g Tyres). Also used in printers, toners etc. It is AMORPHOUS form of carbon, that is without definite shape.
Nano particle: Anything of size in the order of 10^-9 metre is a nano particle. CBNP's are considered carcinogenic as they kill cells in our lungs on prolonged exposure. Currently research is on to link its contribution to global warming too!
Carbon black, in my opinion, is INORGANIC. Carbon black has Graphite content that varies depending on the process of its production. Graphite in turn is considered Inorganic despite being an allotroph of carbon (IUPAC Red book). Most carbon-containing compounds are organic, and most compounds with a C-H bond are organic. Not all organic compounds necessarily contain C-H bonds