In the past 4 months, a family member has had colon cancer surgery, a permanent catheter, chemo, a severe UTI and 3 hospitalizations. Is it appropriate to diagnose him/her at age 83 with dementia when he/she has never forgotten a friend or family member's

Probably not. When chronically ill, someone can at least temporarily lose cognitive functions they previously had, or have dysfunction in memory, concentration, judgment, etc. With what your relative has been experiencing it's possible his/her mental functioning could be impacted (delirium). This is treated by addressing the underlying medical causes, and hopefully previous functioning will return.
Probably not. Probably not the best time to diagnose dementia with many other comorbidities.
Question. I am not clear what your question is since you have not mentioned dementia symptoms such as memory loss or difficulty communicating, learning, planning, or organizing. Your "relative" has gone through a lot so if there are memory problems it may be secondary to medical problems/procedures. If dementia like symptoms appear and remain, a psych evaluation is indicated.
No. Chemotherapy and the related stress of treatment can definitely affect memory and recall also it is inappropriate to worry about the dementia or diagnosis of dementia and cruel when the patient is fighting with chemotherapy against cancer.
DEMENTIA. Patient underwent a lot of trauma. From cancer surgery, chemotherapy, severe UTI and 3 hospitalizations. At this age, dementia sets in aside from the above medical problems. Gather yourselves , kneel and say a prayer of thanks to god that he is still alive and has only memory loss or dementia.
Medical ethics. Did the person has health care proxy ? If signed has to follow the instructions, if no signed health care proxy, & living will courts will decide, what extent the treatments to be rendered. Ask 101 yr old marathon runner, is 83 is too old, so age should not be the issue, quality of life is issue, usually such instances both family and medical team will discontinue aggressive treatments ref to hospi.