In TES Lore, Arkay is considered one of the youngest dieties. This is because his sphere - the cycle of life and death - didn't even exist until after the other seven divines created the mortal world.

Well, if that logic holds, then that begs the question of where Meridia came from. She is a Daedric Prince, meaning that her existence had to predate Nirn (that's the definition of Daedra: Those who didn't take part in the creation of Nirn), and yet, she dirives her power from the energy of living things.

However, such a distinction was never made prior to the creation of Nirn. So... where did her power come from beforehand?

Daedric Princes do not need prayers for power, IIRC. The prayers are more like a power up. Aedra lost almost all their power during the creation of nirn, so they need prayers.

I cannot answer the answer in the title for sure, but I think that Meridia was created around the same time the other aedra and daedra were created.

OP didn't mention prayers.

There were no "living" things before creation. That's what he/she is saying. It's paradoxical, an entity that derives power from life, that existed before the very concept of life was possible.

Meridia was a Magne-Ge, an aedroth in Aetherius. Most specifically she begun as a constellation.

But there were a war in Aetherius, Meridia was the leader of the constellations against Magnus.

Magnus won the war, Meridia was banned into Oblivion, and new constellations take place.

Source : http://www.imperial-library.info/content/magne-ge-pantheon, and http://www.imperial-library.info/content/imperial-census-daedra-lords.