Analysing and interpreting results of functional connectivity

What is the best way to test the statistical difference between the two conditions

Non-parameteric paired test across subjects (FilesA=Condition 1, one connectivity file per subject; FilesA=Condition 2, one connectivity file per subject)

do I as suggested in the tutorial- average the connectivity matrices for the two conditions and run a test of difference of means, or is there a better way?

What tutorial are you referring to?

When I take the average of these two conditions for all subjects and compute the difference between these two averages- how do I interpret the resulting graph?

Differences of connectivity measures after difficult to interpret directly.
What you are interested to know is whether these differences are significant across subjects.

Is there any reading material/ publication from where I can get further details on these methods for my own understanding as well as the publication I intend to write from these results.

https://neuroimage.usc.edu/brainstorm/Tutorials/Connectivity2#Envelope_correlation_.282020.29
https://neuroimage.usc.edu/brainstorm/Tutorials/Connectivity2#Additional_documentation