For example, a person committed tawbah for shirk, repented never to return to it, but at the same time he commits other sins. (Listening to music, watching movies, committing adultery) Would his tauba be valid?
Yes. Al-Nawawi said:
Tawbah will still be valid even if you were persistent on other evildeeds, as Ulama explained, so if someone steals and commits adultery, him being persistent on adultery does not affect his tubah from stealing and vice versa
(from Arabic original)
Most of Ulama agree on this view (See Ibn Qayyim in Madarij Al-salikin). Also See Al-Qurtubi's Tafsir for An-Nissa:17:
Tubah is valid with having another sin of a different nature, unlike what Mu'tazilites think: you can't have tubah when you have a sin.
Note: Listening to music, watching movies cannot be considered as sin, it depends on type of music or movies you hear or watch.
It is human nature to incline towards sins and best of sinners are those who repent.
Anas (RAA) narrated that Allah's Messenger (ﷺ) said: “All the sons of Adam are sinners, but the best of sinners are those who repent often.” Related by At·Tirmidhi and Ibn Majah with a strong chain of narrators. https://sunnah.com/bulugh/16/41
Sinning doesn't necessarily mean doing forbidden acts like theft, adultary but also include not worshiping enough. It is said that if we count the blessings of Allah it is not countable.
And if you should count the favors of Allāh, you could not enumerate them. Indeed, Allāh is Forgiving and Merciful. Quran 16:18
So how much we worship Allah it is not sufficient. So we need to continue to do tawbah (seek forgiveness).
Allah's Messenger (ﷺ) said: "By Allah, I seek the forgiveness of Allah, and repent to Him more than seventy times in a day. https://sunnah.com/hisn:248