List of Object properties
Is there a function or system view that returns all of the available
  property names?


No. There isn't even something that returns the names of all of the available built in functions (such as OBJECTPROPERTY itself).

These property values are documented for OBJECTPROPERTYEX even though they do also appear to work for OBJECTPROPERTY and probably should be documented there (the return type is int so there is no reason that they shouldn't be supported there and it is more convenient to work with that function without needing a cast from sql_variant.)

For entirely undocumented property values (such as minlen for INDEXPROPERTY) I'm not aware of any way of determining these.