Is it permissible to browse Facebook and social media sites while watching television, or forbidden series or movies, if the majestic name of Allah or Quranic verses appear? And what is the ruling on remembering Allah inwardly while watching what is forbidden?

The one who views forbidden images must hasten to repent and immediately cease doing so. Browsing Facebook or similar platforms while viewing these images, with the possibility of God's name or Quranic verses appearing, is permissible, provided Facebook itself is free of religious transgressions. Remembering Allah in the heart without uttering it aloud is not considered dhikr (remembrance), which is why a person in a state of janabah (major ritual impurity) is permitted to recite the Quran silently in their heart. Consequently, remembering Allah in the heart while viewing some forbidden things is not prohibited; what is prohibited is viewing the forbidden things themselves.