What is the ruling on one who finds it difficult to balance between their work, personal life, and religious duties? And is it permissible for them to delay Fajr prayer until work hours if staying up late leads to missing its proper time?

Work is a blessing and commanded for earning a livelihood and becoming independent of others. A Muslim is required to maintain acts of worship, especially obligatory ones like prayer at its prescribed time, even with long working hours. Time can be organized by sleeping early and prioritizing so that family, children, and rest are given their due rights after prayer. What your friend is doing by abandoning prayer is impermissible, and he must be advised. As for occasional matters, specific times like holidays or a short period should be allocated for them.