Hi Jed, yes, of course we need to clarify what we refer to as "hunger". In my view it is only hunger if it affects people's functioning and therefore has a negative impact on their productivity and well-being, reducing their capacity and capability to study, work, take care of their dependents, etc. It exactly this loss of functioning that is measured by summary measures of population health, such as DALYs. (Or is there also "hunger" that has no negative mental or physical health consequences?)
Regarding measuring the immediate past vs. capturing a stock of health, at least for the calculation of the original DALYs incident rates are used and not prevalence rates, i.e. the entire health loss due to a chronic condition (such as stunting due to zinc deficiency or blindness due to vitamin A deficiency) is counted at the year of onset (with the loss being calculated over the average expected life expectancy of the individual). Short-term outcomes, such as malnutrition-related night-blindness, diarrhoea, or loss of stamina are anyway counted in the period of observation. Hence what matters for these measures are only single periods of observations, not longer periods.