In a newspaper, issues in a community would be found in:
• editorials
• columns
• letters to the editor
The meaning of Gwendolen's words is that she is against the traditional idea that women are the ones who should stay at home to be in charge of the domestic duties. She shows that women might have a position of power and that men can stay at home.
The literary technique used is Paradox because Gwendolen proposes a reversal of the traditional and well-known ideas.
I believe it's false but I'm not 100% sure.
