Maximum biologically possible age for a human being?
Even in perfect environmental conditions we would age. Living is associated with a myriad of deleterious processes, both random and deterministic, which are caused by imperfectness, exhibit cumulative properties, and represent the indirect effects of biological functions at all levels, from simple molecules to systems. Here is a good read on this topic https://www.ncbi.nlm.nih.gov/pubmed/27060562

Even if nothing else was wrong (which is not the case) the accumulation of intracellular and extracellular junk which our systems are unable to dispose of (lipofuscin, amyloid beta, etc) would eventually kill us. https://en.wikipedia.org/wiki/Senile_plaques

As for the maximum age - nobody we know of made it past 125 years yet. https://en.wikipedia.org/wiki/List_of_the_verified_oldest_people