Which characteristics of carbon are responsible for the existence of a large number of organic compounds;

Catenation is the property of bond formation with atoms of the same element. Group 14 elements show catenation property. Carbon has a tendency to bond with other carbon atoms.

Carbon forms multiple bonds by lateral overlapping of orbitals. This property also helps in a large number of bond formations.

Isomerism is the phenomenon of compounds having different structures but the same molecular formula. Hydrocarbons are any carbon compounds that only include carbon and hydrogen. Isomerism results from variations in the structure of the carbon chain that makes up the molecule's nucleus. We are aware that isomers are defined as molecules having the same chemical formula but a distinct atomic configuration or atom connectivity. Structural isomerism is the occurrence in which the molecules in which the atoms that generate the isomers are attached differently. 

Thus all the given options cause a large number of hydrocarbon compounds.

Hence, option D is correct.