delete vector of objects, single objects, dealocate menory

[laserlight]

This is what is happening by doing newSet = dataSet();, more or less?

Yes, except that having tempSet is unnecessary.

Does my copy constructor need to have a default value for all the member variables?

Your copy constructor? I would expect the copy constructor to copy everything, except in special cases.

What happens to the string and vector variables if they aren't initialized to a default value.

If you did not initialise them explicitly, they will be default constructed to empty string and empty vector, respectively.

Will assigning a default constructed object clear and de-alocate that memory?

If you implemented the copy/move assignment operator correctly, or if the compiler generated one will suffice, yes.