Could not fit in a comment..
The question is off-topic
Biology is the study of life. Without a good definition of life, Biology itself is poorly defined. It appears that there is no universally accepted definition of life and therefore Biology (just like Chemistry and Physics to cite other examples) is a poorly defined field of study. But it is not scientists job to decide whether their work should stand within one category or another, nor whether those categories are natural categories (see prototype theory) or not. It is the job of philosophers and therefore this question is about philosophy and is off-topic here.
Few notes about the definition of life
Most often, philosophers see a continuum from not living to living things and not a clear dichotomy (ref.).
Biologists, most often just assume that bacteria, archea and eukaryotes are living things while viruses, viroids and prions are not living things. This arbitrary dichotomy is based on the concept of metabolism. However, this dichotomy can lead to some limit cases. Typically, considering viruses as not being living things yields to intuitive issues when thinking about macroviruses such as Marseillovirus and Lausanevirus.
There are two questions in your post
Of course, the definition of what is dead is a total different question from the question of what is a living thing. A stone is not dead it is just not a living thing. Even then, the definition of death is of interest to philosophers, not to biologists. You should always try to limit your post to a single question.