Only the generic mana in that creature's mana cost is reduced. For example, if that creature's mana cost is , you'll have to pay to keep it.

The creature enters the battlefield, so it will trigger enters-the-battlefield abilities even if you choose not to pay.

If the creature has in its mana cost, X is considered to be 0.

If you choose not to pay, the creature is sacrificed immediately. No player will get priority in between the creature entering the battlefield and being sacrificed. Sacrificing the creature this way will trigger any abilities that trigger when it leaves the battlefield, and those abilities will be put onto the stack at the same time as those that triggered when it entered the battlefield.