Find me in water, I'm mostly grey.
mullet - a fish, the grey mullet is common
At the Spanish South I am red.
red mullet - found in warm seas, notably the Mediterranean
Coming down from the sky, I'm a lizard,
land mullet - a large lizard of the skink family, to land is to come down from above
And notably worn on the head.
mullet - an embarrassing hair style, see Bono or Bowie
I am a star with rays that are straight.
In heraldry a mullet is a star with straight-sided rays
Near a crystal river lies my key.
Mullet key - a historic island near Crystal River, Florida.
On reflection, my style is emo.
Tellum - a reverse mullet, short at the back, considered an emo style
A Caesar directed me.
Mullet - an Australian film directed by David Caesar
Title: Think Deeply About It
Sounds like mull (think deeply) over it