Okay, so you've got a battery, but the problem with batteries is that the battery itself has some resistance, which is internal resistance, which you probably already know.
So what you've really got is a circuit which looks like this:
.
R1 is the internal resistance of your battery, and the 'voltage' you're measuring is the voltage across R2.
You can work out the EMF of the cell by drawing a line from the points given on the graph and looking at the x-intercept, which turns out to be 1.6V.
For b.), if you look at the y-intercept of the graph, you get a current when there is no voltage across the output; that is, when all the voltage is going across the battery's internal resistance. Using
, we get a value of
for R.