Seneca - Yes, separation of church and state is a spectrum with perhaps Iran on one end and France on the other, but US really does not have much of it. As I said, the official motto of the US is "In God we trust".
"Constitution provides that there be no establishment of religion which, through the years, has been interpreted rather broadly."
Sorry I don't understand what this means. "There can be no establishment of religion"?
"The constitution also provides for the free exercise of religion so that comes into the equation as well."
Nothing to do with the concept of separation of church and state.
"in state schools, there can be no religious observances like school-sponsored prayer or nativity plays"
But talk of God is everywhere and Pledge of Allegiance is often recited in American schools with the line "One nation under God".
And that God is the Christian God, not any deity or spiritual power that Americans might believe in.
There are Muslim countries where state is less entangled with the dominant religion.