To me the English sentence is not a natural sentence in the present-tense form. When would an English speaker say that?! It is much more natural in the past:
We finished eating the apples.
So this is "we finish to eat the apples", literally? I guessed right but it's a little clunky for a native English speaker. Would be nice to have this syntactical rule spelled out.
Not sure because since finiĝi means to come to an end; concluding; end; etc.. Maybe something like we ended eating apples, but I not exactly sure, though