a) What is the unit of atomic mass?

Since 1961 the unified atomic mass [u] is defined as 1/12 of the mass of one atom of nuclide 12C which has been assigned to 12 u exactly by convention.

b) Do you have an estimate of the magnitude of the masses mass spectrometry deals with? Calculate the molecular weight of some typical small molecule in units of kilograms.

1 u is obtained by dividing the mass of 1 mol 12C by the number of atoms (Avogadro’s constant):

1 u = 0.001 kg/mol / 6.022 x 1023 = 1.666 x 10-27 kg

Thus, a molecule of CO2 has a mass of 7.330 x 10-26 kg, for example.
In general, molecular masses are in the range of 10-26 to 10-23 kg.

c) Can you tell m/z, Thomson, u and Dalton apart?

Some mass spectrometrists use the unit thomson [Th] (to honor J. J. Thomson) instead of the dimensionless quantity m/z. Although the thomson is accepted by some journals, it is not a SI unit.
In particular mass spectrometrists in the biomedical field of mass spectrometry tend to use the dalton [Da] (to honor J. Dalton) instead of the unified atomic mass [u]. The dalton also is not a SI unit.