1. The boiling point of oxygen is about 90 kelvin (13 degrees higher than nitrogen's boiling point). If the liquid around a cryo-patient is not changed over time then we might expect the ratio of liquid oxygen to liquid nitrogen to increase over time. Is the presence of the liquid oxygen relevant to rancidty issues or not?

probably not:

At the temperature of liquid oxygen, most bimolecular chemical reactions are largely inhibited. The rates of these reactions, in general, decrease rapidly with decreasing temperature. At very low temperatures the rates become too small to be measured, and for practical purposes it may be said that reaction ceases. This is especially true of oxidations, since, for example, neither sodium nor phosphorus immersed in liquid oxygen undergoes any apparent oxidation.