organic chemistry - Nucleophilicity/basicity in protic and aprotic solvents

1. 
   

   In polar aprotic solvent, why is $\ce{F-}$ a stronger nucleophile than $\ce{I-}$?

   
   

   What I think: If I talk about their basicity, $\ce{F-}$ would be more basic due to instability from its high electron density. Is it applied same when talking about nucleophiliicty?

   
   
   


2. 
   

   Why is an atom with high polarizability a strong nucleophile?

   
   

   What I heard: an increased atom size means a high polarizability, and a high polarizability means a high nucleophilicty because the atom can give its weakly-held $e^-$ easier.

   
   

   What I think: above sentence makes sense to me. But in another point of view, isn't it also right that the atom with properties like that would be stable, making it poor nucleophile?

   
   


3. 
   

   When talking about nucleophilicity, why does the polarizability matter in a polar protic solvent, but not in a polar aprotic solvent?

   
   

   What I heard: when deciding the nucleophilicty of an atom in a polar protic solvent, there are two factors that come into play: solvation and polarizability.

   
   

   What I think: in a polar protic solvent, since the effect of solvation is significant, the polarizability shouldn't mean so much. Rather, its effect should be significant in polar aprotic solvent since there's no hydrogen bonding. Is this wrong?