in through looking glass, why the characters act the way they do, and what does the behavior say about alice?

Alice is in fact alone through much of the story, though not as much literally as figuratively. She is the only one of her kind in the Looking-Glass world, so even though she is surrounded by creatures pretty much at all times, she has trouble relating to their foreign ways. She is also isolated from the rest of her family due to her imagination; there is a reference to the frustration she causes when she plays pretend. At many points in the story, the reader has the sense that Alice has no place to go to feel at home; she expresses her loneliness while in the Looking-Glass world, but she immediately rebounds and worries about ultimately having to end the game and return to her house.