How do antioxidants work?
1) solubility. Typical liquid fuels consist entirely of hydrocarbons and are non-polar and thus cannot dissolve polar molecules like ascorbic acid.

2) The molecules mentioned in the provided quote can form stable radicals on loss of $\ce{OH}$ group hydrogen, i.e. act as a radical trap, transforming active radicals into non-active particles. It is a typical mechanism for antioxidants to work.

3) Strongly depends on the definition of effectiveness employed. Differen applications demand different properties.

4) Because in industry people typically do not bother with isolation of individual products if a mixture can work just as well. Sure, one can isolate individual products of phenol alkylation, but it is a tiresome work, so why bother, if the mixture works just fine?