Diablo – ny limitation as to which character can identify an item in Diablo 3

If you're talking about the Jar of Souls or Matriarch's Bones quests that randomly appear in one of the incorrect defiled crypts, then no. These quests are simply random and can appear on any difficulty or hardcore setting.

It remains to be seen for the rest of the game, I don't know of any specific answers that have been given out by Blizzard staff mentioning hardcore-specific quests.

The only difference between the gendered classes are aesthetics, both in visual appearence, and in audio voiceovers / text. (Mostly pronouns)

The individual stories for the classes (the parchment-style cutscenes that play on the completion of most major quests) also vary between the genders.

Perhaps the biggest differences are in the dialog between the player character and their follower when playing solo. When interviewed about it, one of the Blizzard devs said that he particularly enjoyed the dynamic between the Scoundrel and the female Wizard.