The validator is slashed in both cases if I’m not mistaken, maybe @djrtwo can confirm. There is no reason/explanation for a validator to vote in a way illustrated on the left.
Neither. When I say “it’s not on the winning fork” I mean “she will not get a reward because she voted for a checkpoint that will not get 2/3 votes, so no reward”.
Hope this helped. 
P.S. You can also skim through this article, it’s nice. 
P.P.S. @dlubarov noticed that Condition II is stricter then necessary, and proposed a nice tweak to fix it (it passed @vbuterin’s QC ).