  The scattering equation formalism for scattering amplitudes, and its stringy
incarnation, the ambitwistor string, remains a mysterious construction. In this
paper, we pursue the study a gauged-unfixed version of the ambitwistor string
known as the null string. We explore the following three aspects in detail; its
complexification, gauge fixing, and amplitudes. We first study the
complexification of the string; the associated symmetries and moduli, and
connection to the ambitwistor string. We then look in more details at the
leftover symmetry algebra of the string, called Galilean conformal algebra; we
study its local and global action and gauge-fixing. We finish by presenting an
operator formalism, that we use to compute tree-level scattering amplitudes
based on the scattering equations and a one-loop partition function. These
results hopefully will open the way to understand conceptual questions related
to the loop expansion in these twistor-like string models.
