You have to look at which side of the reaction the electrons are on. If they are on the product side, then the reactant is getting oxidized (losing electrons) and is therefore acting as the reducing agent.
If the electrons are on the reactant side, then the reactant is getting reduced (gaining electrons) and is therefore acting as the oxidizing agent.
Regardless of which half potential you are looking at, if the Ecell number is negative, the reaction is less likely to happen. So since 2F- ----> F2 + 2e- has a negative Ecell number, 2F- is probably not going to get oxidized, and therefore 2F- will not act as a reducing agent.
For Au and Hg they switched the reactions around on you (look at where the electrons are!). Both Au3+ and Hg2+ have positive reduction half potentials, so they are readily reduced and will act as oxidizing agents (Au3+ more-so than Hg2+ since the Ecell is more positive for Au3+).