Let's go though the choices.
Major axis will get shorter. TRUE, CHECK ME
As the plane moves closer to the vertex the ellipse stays the same shape but shrinks.
Ellipse will become a circle. FALSE
As long as the plane is tilted, the ellipse can't be a circle.
Ellipse will degenerate to a point. TRUE, CHECK ME
Eventually the plane gets to the vertex, at which point (ha!) we have a single point.
Nappes? Is that a word? FALSE
The plane needs a steeper angle, steeper than the generators, before it can pass through both halves.
The generators are the lines through the vertex that form the cone. The plane isn't steep enough to hold any of them. FALSE