1.  What is the relationship between the average product curve and the 
average total cost curve 
 
2.   Why might a firm continue to produce in the short run even though the 
market price is less than the average total cost

You may want to check the wording of the 1st question, as "average
product curve" doesn't make sense.  Could it be "average product price
curve" or "average product variable cost curve"?

yes it is average product price

sorry it is average product price curve

Hmm....so your question becomes 

1.  What is the relationship between the average product PRICE curve
and the
average total cost curve?

Is this correct? 

(I'm confused I've not come across an 'average product price curve'
but an 'average product curve' is common)

Hi

yes - it is correct - I am confused my-self when I found this question
in the Economics text books

This is indeed interesting, maybe they both mean the same thing, just
that the words are different? The 'average product curve' I'm familiar
with has a graph with 'amount produced' on the y axis, and 'labor
needed' on the x axis... well, maybe someone can shed some light...

I am in the process of finding out the relationship between the two
curves.  However can someone answer question 2.