Story-telling technique where the drawing style briefly gets much simpler?
It's called an Art Shift, traditionally used in western media for homages, parodies, or flashbacks; e.g. Tracer Bullet or when Calvin and Susie play house in Calvin and Hobbes. These art shifts usually last for one or more scenes, often for the duration of a specific subplot. The Japanese use art shifts in a very different way-- single-shot/panel shifts are quite common in anime and manga, and are used for comedic emphasis. Kimi ni Todoke, for example, uses this quite frequently (Kimi ni Todoke vol. 10 / ch. 42 spoilers). It is often used in conjunction with other anime/manga tropes (Cross Popping Veins, Dull Eyes of Unhappiness, Giving Up the Ghost, Nosebleed, Snot Bubble, Sweat Drop, Visible Sigh, Kewpie Doll Surprise, etc.) to convey emotion humorously, or on a specific character to show that they're acting in a way that's different from the rest of the world. It can also be used on a group of characters to show a sudden (and usually temporary) shift in tone.  Shifting into a chibi art style usually implies a comedic or moe tone.

As to your specific examples, the art shift creates an emphasis on joke-- in the first example, how Faye is forced to subvert her usual threats of violence, and in the second example, how Faye completely misssed the point.