1) If one is reciting namaz and there is Quran being recited on TV is the Namaz valid?
2) If one has verses of the Quran written on a piece of paper is he allowed to go in the washroom with it?

1- Yes the Namaz is valid.
2- Yes he is allowed to go with it as long as in one’s society it’s not seen disrespectful to the Qur’an. In most societies it’s not seen as disrespectful so it’s ok