Is it legal to participate into the TV shows of competitions (cultural competitions) and if I win, is it legal to take that money?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

These cultural competitions are of two kinds:

The first type: Competitions about religious knowledge, like about the Qur'an and the narrations of the Prophet and anything that has a relation to this. The jurists differed in opinion about taking compensation in such a competition. However, the most preponderant opinion on this matter is that it is permissible as we have previously stated in Fatwa: 83439. 

The second type: Competitions about other subjects other than religious knowledge; it is not permissible for such competitions to be held for compensation and it is not permissible to accept a prize obtained from such a competition, because Islam only allows taking compensation in competitions of horse racing, camel racing, and archery, and in similar competitions that strengthens one's religion and benefiting from the saying of the scholars.

Allaah knows best.