Is the mass of the proton about one atomic mass?

Answer 1

No. Different elements have different atomic masses, the all protons have the same mass (ignoring the small mass loss to binding energy when bound inside an atomic nucleus).

The Atomic Mass of an element is the weighted average of the atomic masses of all isotopes of that element. The atomic mass of an isotope of an element is the sum of the protons and neutrons in its nucleus, minus the mass loss of the protons and neutrons to binding energy, plus the mass of the electrons around the atom (but their mass is so small as to usually be negligible and is ignored).

The element hydrogen has one isotope whose nucleus is just a single proton, all other elements have both protons and neutrons in their nuclei. Only for this hydrogen isotope is its atomic mass about the mass of the proton. The mass of its proton nucleus is not reduced by binding energy, as there are no other particles in the nucleus for the proton to bind to and the mass of the single electron in the atom is about 1800 times smaller than the mass of the proton making it negligible in the total atomic mass.