The only other way I can see you calculating the residuals without reading from the graph is if the question also gives you a set of actual values. Which you would then use to create a regression line. From there its simply the case of
residual value = actual value - predicted value
Though I am quite sure you won't be asked to determine the residual from the graph alone, especially if its hard to make out the points (I haven't crossed any questions that do this...well at least none come to mind).
And no they are not the same.
A log
10(y) is called a log transformation whereas a 1/y is called a reciprocal transformation.
Basically they serve the same purpose, its just that the reciprocal transformation compresses the data to an even greater extent than the log transformation.
hope that cleared some things up somewhat