Is money earned from working in a hotel kitchen that serves alcohol, without touching or carrying it, unlawful? And is it permissible to recite adhkar and the Quran without adhering to prayer, such as performing it outside its prescribed time or sometimes abandoning it?

If the questioner's work is not related to alcohol, then his work and earnings are not forbidden to him, but they are disliked due to the inclusion of a percentage of alcohol in the hotel's profits.

There is no objection to reciting the Quran and performing remembrances for someone who has delayed prayer or missed some of them. Rather, the real objection lies in delaying prayer itself or missing some of its obligatory parts, as this is a major sin. No one is excused for missing prayers, even under work circumstances. The questioner's need for this job might be a consideration for combining prayers, but there is no excuse for abandoning some of them entirely.