How long can a dementia patient live?

No single answer. There are several types of dementia , like any other sever illness they are associated with decreased life expectation. It varies a lot, i.E creutzfeldt jacob dementia life expectation is counted in months while that of alzheimers dementia can be years. It is also affected by the general medical care available to the patient suffering from it. I hope this answers your question.
Although varies. Most studies on the alzheimer patient suggests a life span of 10-15 yrs following onset of disorder.
Depends. Factors include the age of the person, their general health otherwise, the type of dementia and how aggressive one is with medical interventions.