1. To be demanding is to want lots of attention from others. It is also to have many needs that need to be met. It is to feel entitled to the attention of others and claiming more than others. A demanding character would be one which is very dependent on others, and always asks for favors or demands favors.
2. “You must create a female version for me, with whom I can live in the interchange of those sympathies necessary for my being. This you alone can do; and I demand it of you as a right which you must not refuse to concede.” (Frankenstein)