are neutron stars made of element zero?

you're the only person I know who claims
.. "element zero is said to be an element with atoms composed of neutrons"

the definition I use for an atom is this
.. "an atom is a small particle of matter consisting of a nucleus containing
.. .at least 1 proton surrounded by a field of electron density"

IUPAC uses this definition
.. "Smallest particle still characterizing a chemical element. It consists of a
... nucleus of a positive charge (Z is the proton number and e the elementary
... charge) carrying almost all its mass (more than 99.9%) and Z electrons
.. .determining its size"
https://goldbook.iupac.org/html/A/A00493.html

both those definitions require AT LEAST 1 proton.

Neutron stars don't have atoms

There is no "element zero". If it doesn't have at least one proton, it's not an element.

much of modern physics seems like an act of faith to me
but maybe the answer is yes
see
https://www.livescience.com/57614-is-there-an-element-zero.html