Are all atoms (elements) neutral? And if not, how is the amount of electrons discovered?

No, not all atoms are neutral. Ions are atoms with an electrical charge, whether it be an anion (-) or cation (+). The oxidation state can be found reliably in groups on the periodic table (exception being rare earth metals and transition metals), or by using the known charges to balance with the unknown ion in chemical reactions.

No not all elements are neutral some are very active and they have the same number of protons as the number of electrons or else it would be an ion which would have more protons than electrons