No, two atoms cannot have the same atomic number but different masses or charges. The atomic number of an atom is determined by the number of protons in its nucleus, and it defines the element to which the atom belongs. In a neutral atom, the number of protons (which is equal to the atomic number) is balanced by an equal number of electrons, resulting in a net charge of zero.
The mass of an atom is determined by the combined mass of its protons, neutrons, and electrons. Protons and neutrons contribute to the majority of the mass, while electrons have negligible mass. While atoms of the same element can have different numbers of neutrons (resulting in different isotopes with varying atomic masses), the number of protons, and hence the atomic number, remains the same. Isotopes of an element have the same atomic number but different atomic masses.
In summary, the atomic number uniquely identifies an element and remains constant for all atoms of that element. Variations in atomic mass occur due to the presence of different isotopes, but the atomic number and charge remain the same for atoms of the same element.