The number and arrangement of electrons determines the?
What determines how atoms (and molecules) combine is their electron configuration. In particular, what matters most is what the number (and arrangement) of electrons in what is called the valence shell of the atom. These are the outer-most electrons, and it is these that determine how things react and combine with other atoms and molecules
Atomic number is the number of protons in the nuclei of the atoms of an element. It is the number of protons that determines the atomic number. In a neutral atom, the number of electrons equals the number of protons. So in a way you could say that atomic number determines the number of electrons in a neutral atom.