1. Discarding a card is a cost which happens prior to activation. The effect doesn't actually occur until resolution so yes you can discard a harpie lady and then revive it. That being said, there must already be at least 1 harpie lady in your graveyard in order for this card to be activated.
2. Cyber Harpie Lady and Harpie Ladies 1, 2, and 3 are always named Harpie Lady all the time. That is why you can only have any combination of 3 of them in your deck (you can't have 2 Harpie Lady 1 and have 2 Cyber Harpies). Because the card is named Harpie Lady it can be revived by Hysteric Party.
3. It is a continuous trap which means it remains face up on the field and does not get placed in your graveyard after activation. You cannot reactivate the trap by discarding another card, however. If it were that way, it would say something to the effect of "once per turn". You only activate its effect the 1 time. That is also like saying you could re-use Call of the Haunted in order to summon every monster from your graveyard.
