When you have multiple “Helpoemer” cards in your Graveyard, each with an activated effect, the effects are cumulative.
If your opponent chooses not to conduct a Battle Phase, there is no timing for the end of the Battle Phase, so the effect of “Helpoemer” is not activated. The same is true if the Battle Phase is skipped due to a card effect.
“Helpoemer” cannot be Special Summoned from the Graveyard even if it was not destroyed as a result of battle (the final sentence on “Helpoemer” is a condition, not an effect, and is not subject to the first sentence on “Helpoemer”).
Netrep Rulings:
“Helpoemer” may not be Special Summoned from the Graveyard for any reason. “Helpoemer’s” ‘discard 1 card’ effect only activates if it is destroyed and sent to the Graveyard as a result of battle.