If you cast a card "without paying its mana cost," such as with suspend, you can't choose to cast it for any alternative costs
It doesn't copy whether that artifact is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, or so on
If a creature with a boast ability is put onto the battlefield attacking, it was never declared as an attacker
The drawback isnt as bad as it looks, and the downside will likely be turning Call of the Full Moon into a two-mana Lava Spike with some chance of repeating
Notice how the black of the mana symbol and surrounding text are made of rosettes, and not black throughout