Looking for clarification on how to draw the arrows for an abstract class which contains private variables of a different class type (i.e. non-primitive variables). I've got this as an example and was not sure if correct.
Image: 
Is this correct?
Looking for clarification on how to draw the arrows for an abstract class which contains private variables of a different class type (i.e. non-primitive variables). I've got this as an example and was not sure if correct.
Image: 
Is this correct?
Rather than Realization which is meant more for interface realization you should use simple Generalization with a solid line instead. This is about inheritance where the concrete inherit from the abstract classes. This means also that the association is inherited which for a realization would not be the case.
Since Christophe mentioned it: There is no need to repeat operations/attributes in the inheriting class. See pp. 100 of UML 2.5:
Members that are inherited by a Classifier may be shown on a diagram of that Classifier by prepending a caret ’^’ symbol to the textual representation that would be shown if the member were not inherited. [...] Inherited members may also be shown in a lighter color to help distinguish them from non-inherited members. A conforming implementation does not need to provide this option.