Here are my answers. Sorry for the delay, I had some troubles to find the information for the first question ^^

> I don't fully understand paragraph 3 of section 4.1.
I know how to calculate the summing of pTs using the sumIsolation method, but I don't know what I'm supposed to do with the results.
What is the isolation criteria?

Unfortunately, the experimental documentation is often incomplete. You found one proof (an d there are many!) by yourself. After digging a little bit, the information is actually hidden in table 3 of [**this paper**](https://arxiv.org/abs/1502.02702). 

> Paragraph 4 seems to indicate 2 lists of cuts, one for "low pTmiss category" and one for the "hight pTmiss category".
Does this mean that the program should be supplied a configuration to indicate which category to apply in the analysis?

You should declare two signal regions (in the initialization part of the code) and then declare the cuts and associate them with one of the regions, the other region or both regions. You can then apply them sequentially. Examples of codes can be found [**here**](http://madanalysis.irmp.ucl.ac.be/wiki/PublicAnalysisDatabase), if needed.

> Does pT1 mean the transversal momentum of the leading photon, and pT2 mean the transversal of the subleading photon?

That is correct. Again, they could have specified it in the experimental paper... (Do you believe I am often arguing about the documentation being incomplete, unclear, confusing, etc?)

> Should an event be selected if a diphoton passes all the cuts in one fiducial region, but none pass the cuts in the other fiducial region?

The code will automatically proceed as long as an event populates at least one region.