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No, Elesh Norn's static abilities have no effect on the battlefield in that case.
Bringing Elesh Norn into play with Flash and deciding whether or not to sacrifice it is all part of Flash's resolution. Killing creatures with her -2/-2 would require state-based effects to be checked, but that only happens after Flash has finished resolving, at which point Eles Norn is already gone.
If you sacrifice a creature brought into play with the spell Flash, basically all you get are "enters the battlefield" and "leaves the battlefield" effects.
No, since no player receives priority between Elesh Norn entering and leaving the battlefield during the resolution of Flash. State-based actions that would place creatures with 0 toughness in their owners graveyards, are not checked until just before a player would receive priority. Rule 704.4 gives a nice example of a creature that has 0 toughness temporarily, that isn't sent to the graveyard, because its toughness is greater than 0 the next time it would be checked.