How long can an 84 year old survive after recently having been diagnosed with copd?

Depends... COPD is a slowly progressive disease. The rate of progression is determined by many factors including age, disease severity at diagnosis, whether smoking is continued, presence of other disease states, etc. In order to answer this question for a particular person, see your doctor so the case specifics can be reviewed!
It depends. It depends on the severity, frequency of exacerbations, oxygen requirement, associated symptoms such as fever, cough etc if at 83 , symptoms are worsening, the prognosis is bad probably within five years.
Years. Depending on how severe their disease is, and what other problems they have, of course. Even patients with severe disease who stop smoking, wear their oxygen (if needed), use their inhalers, and do initially supervised exercise can live for years. If their overall health is poor, and they don't want to stop smoking, their life expectancy is lower, of course.