Any change to a land's type or splicing of text into a land can affect the types of mana a land can produce.

Any replacement effects are considered by Reflecting Pool when determining the types of mana a land can produce.

Reflecting Pool doesn't care about any restrictions or riders your lands put on the mana they produce, such as Pillar of the Paruns and Hall of the Bandit Lord do. It just cares about types of mana.

Reflecting Pool checks the effects of all mana-producing abilities of lands you control, but it doesn't check their costs. For example, Vivid Crag says "{T}, Remove a charge counter from Vivid Crag: Add one mana of any color." If you control Vivid Crag and Reflecting Pool, you can tap Reflecting Pool for any color of mana. It doesn't matter whether Vivid Crag has a charge counter on it, and it doesn't matter whether it's untapped.

The types of mana are white, blue, black, red, green, and colorless.

Multiple Reflecting Pools won't help each other produce mana. If you control a Reflecting Pool, and all other lands you control either lack mana abilities or are other Reflecting Pools, you may still activate Reflecting Pool's ability — it just won't produce any mana.