Can pain make delirium worse?

Absolutely! Very ill or aged folk can have delirium triggered by minor additional symptoms and pain is a common one. Management can be difficult w/out extreme sedation and that can risk or hasten death. But it can pass - it is a mental state - not a disease in itself. Try to keep the situation as calm and peaceful as possible. Try to recall the good times and stories of such a long life - that might help.
Yes. pain causes significant stress on cognitive reserve and the central nervous system. It is a well established cause of delirium. One of the challenges is that pain medicines like opiates can also cause delirium. There is a careful clinical balance that can be difficult to attain. Good communication between the patient, family and medical team is important.
Likely, but. Details are unclear. Indirect evidence and clinically sepaking, yes it can. I suspect the secondary effects of pain on sleep impairment and increased opioid use may contribute. Opioids are not strictly contraindicated however. At times, they may simply need to be rotated. Unclear if inflammatory cytokines precipitate or sustain delirium (acute brain failure).