Yes, all of these factors do affect the degree to which a person saves or does not save.
A rich person will generally be able to save more of their income than a poor or even a middle class person. A person who expects the economy to be strong might be less likely to save because they will feel secure in their economic future and think they can always save later. During a recession, a person might not save as much as during other parts of a business cycle. A person who is past retirement is less likely to save than one who is in their prime earning years. In these ways, all of these factors do affect the amount that an individual saves.