What phases (solid, liquid, gas) are present in the unlighted candle? In the burning candle? Which phase appears to take part in the chemical reaction?

Only the solid phase.

When lit all three phases of matter are present, solid, liquid and gas. The candle itself is still solid. But liquid wax pools under the flame. And the flame itself is releasing gases consisting mostly of water vapor and carbon dioxide. Many consider the flame is in another state of matter, the plasma state. It's a high energy state of matter exhibited by stars, flames and lightning.