It's a suicide method. You make the room air tight with tape (ie blocking airflow of the windows or doors) and then use the charcoal in a portable-stove which will cause the room to fill with carbon monoxide which can kill you. (not advice for dying, just explaining the joke for the chapter).What is the joke about coal and gum tape? This isn't the first time it's shown up.
In the first chapter he was giving them handouts, so presumably they met through the delivery of those.I wonder how the three of them met since Menhera obviously doesn't go to school.