The concept of butch/femme or masc/femme refers to how one presents themselves with regard to male/female gender norms. Things like makeup, heels, and pink are femme, while very short haircuts and sturdy work clothes are butch or masc.
Panel 1: That person is butch.
Panel 3: I will attempt to woo them.
Panel 4: Are you a butch person interested in sexual and/or romantic relations with another butch person?
the mom definitely gives big "the artist usually draws another kind of art" vibes, like when you see something with suspiciously detailed feet or uvuluas