I am looking for an answer to one question here on this site and can't find it.
If I get a retirement visa, can I buy a business, run it and earn income in Spain?
Or does the retirement visa go to retired people who have no right to have income in Spain, even if they are self employed?
No - a retirement visa doesn't allow you to work at all.
You can only buy or set up a business in Spain with an investment visa.