Is the solution after crystal precipitation an unsaturated solution?

Is the solution after crystal precipitation an unsaturated solution?

It's saturated.
Because it is saturated, the excess solute becomes a crystalline precipitate.

Is the mother liquor of salt unsaturated solution after crystal precipitation from seawater? Why? Is the mother liquor of salt unsaturated solution after crystal precipitation from seawater? Why? Why?

It is an unsaturated solution of salt because there are other solutes besides salt (sodium chloride).