The documentation of the results in /graphdata is pretty short.
It seems .nodes.csv contains only the nodes with the node ID being the first CSV column.
Also .edges.csv are the edges. However, for these the edge endpoints vs. edge properties are not easy to automatically convert from the CSV file.

Furthermore, what do the parts mw, hg, se, ce, w mean?

For the casual researcher, just interested in benchmarking a graph tool, mass ingestion of the graph data is the goal.
I'm not a python guy, but this seems to be a standard way to write GraphML in python:
https://networkx.org/documentation/stable/reference/readwrite/generated/networkx.readwrite.graphml.write_graphml.html#networkx.readwrite.graphml.write_graphml