Is it permissible for me to demand a share in the television that my brother bought with money that was jointly owned, given my fear of sharing in the sin of what is broadcast on it? And is it permissible for me to buy it from him?

The questioner incurs no sin by his brother watching forbidden things on television, as long as he does not assist him in it. He is not obligated to take the television from his brother. Rather, his duty is to advise his brother, remind him of Allah, and explain the prohibition of looking at forbidden scenes, in accordance with the Hadith: "Religion is 'naseehah' (sincere advice)."