Delusion is a firm, false belief in the content of the thought. Somatic delusions and hypochondriacal delusions concern bodily appearance and functions. This is close to what you are proposing as physiological delusions.
There are many medical causes of delusions. You can look them up online. Cognitive Dissonance is an interesting term to look up as well. Some political parties seem to have CD where they think things are true when they are not. No one can convince them otherwise even with evidence!!!
It depends on what you mean by 'delusion'. I assume you mean the symptom. Evidence shows that psychiatric symptoms worsen when people don't sleep enough. The brain has much more trouble processing its own emotional, psychological needs and the self when lacks sleep. Also, we have seen patients have more psychotic, depressive and anxious outbreaks in the clinical practice when they don't sleep
Regarding your second question, yes. The way the brain works and the RAS are very influenced by the cyrcadian rythm. We truly are diurnal animals and alterations in this can lead to health and performance issues long-term
It's important that you difference a delusion from an idea of reference. An idea of reference stands the chance of doubt while a delusion is a firm believe. Anyhow, yes, privation of sleep can bring you closest to experience any of those. How great this privation is, is significant to the issue. However, you should also check other indicators, such as genetic predisposition to any type of psychotic disorder/symptom, alimentation, substance intake and socialisation.