Pili-Pala’s ability is a mana ability. It doesn’t use the stack and can’t be responded to.

Using this creature’s ability means you’re untapping it for mana, not tapping it for mana. Mana Reflection won’t cause it to produce extra mana.

If Pili-Pala is already untapped, you can’t activate its ability. That’s because you can’t pay the “Untap this permanent” cost.

If a creature with an ability hasn’t been under your control since your most recent turn began, you can’t activate that ability, unless the creature has haste.