What is the permissibility of listening to Quran, nasheed, latmiyat, etc as a background such as cooking, showering, using the bathroom, and such.

There is no harm in hearing them in the background. For example if the Quran is playing in another room and you happen to hear it while in the bathroom. However, deliberately playing the Quran in the bathroom where you relieve yourself would be seen as a disrespect towards the Quran and one should refrain from anything that disrespects the Quran.