What is the relationship between Working Memory and Attention, and how can one assess his WM? If someone who had low working memory scores as a child suddenly sees in improvement in attention as he grows older, does his ability to hold and manipulate information also increase? Or does attention serve as bottleneck score for such working memory exams?

Also, is there a way for someone to assess his WM at home?
Engle has published extensive papers about this topic and if you are interested I suggest looking him up. 

In 2001 Kane, Bleckley, Conway, &amp; Engle (In Engle, 2002) attempted to directly measure the relationship between WM and executive attention, and conclude that that the underlying factor responsible for the relationship between measures of
WM capacity and performance on higher-order cognitive tasks is a
domain-free executive-attention system. 


  Although individuals possessing different WM capacities will
  show differences in number of items stored in a variety of memory
  tasks, this is a result of differing ability to maintain and inhibit
  information, particularly in the face of distraction and interference.
  Only when the context makes it difficult to maintain the appropriate task
  goal do people with high WM spans perform better than people with low
  WM spans.


In 2003  he found that:


  Individual differences in working-memory (WM) capacity predicted performance on the Stroop task in 5 experiments, indicating the importance of executive control and goal maintenance to selective attention


In my opinion the two are obviously linked however it would be difficult to infer causality or direction in the relationship. It would make sense that if your attention improves your working memory would also improve, however it's hard to say if one causes the other  or if they are intrinsically linked and would just both increase at the same time.  

In terms of measuring WM at home here is a link to an n-back test which I think will be fairly easy to do at home: 

http://cognitivefun.net/test/4

The n-back task requires participants to decide whether each stimulus in a sequence matches the one that appeared n items ago. N-back has become a standard measure for WMC, however treat results with a pinch of salt as Kane et al (2007) have called it's validity into question. 

References:

Engle, R. W. (2002). Working memory capacity as executive attention. Current directions in psychological science, 11(1), 19-23.

Kane, M. J., &amp; Engle, R. W. (2003). Working-memory capacity and the control of attention: the contributions of goal neglect, response competition, and task set to Stroop interference. Journal of experimental psychology: General, 132(1), 47.

Kane, M. J., Conway, A. R., Miura, T. K., &amp; Colflesh, G. J. (2007). Working memory, attention control, and the N-back task: a question of construct validity. Journal of Experimental Psychology: Learning, Memory, and Cognition, 33(3), 615.