Is there any correlation between the level of serum protein and that of ferritin and transferrin since protein molecules are used in making ferritin and transferrin.
In general, I would say no to this.  When the liver
makes more of one type of protein, it sometimes does
so at the expense of another.  When Acute Phase
Reactants are increased (this is in an acute setting),
then albumin is decreased.  This also can occur in
chronic infections.  But I don't think in seeing
increased  transferrin and ferritin levels there is an
automatic decrease in albumin levels. (Remember, in
HH, when the ferritin is high, transferrin tends to be
low)  However, if cirrhosis is present (sometimes seen
in HH patients with very high ferritin levels) you do
see lower albumin levels, but this is due to impaired
liver function, not decreased albumin due to the
increase in another protein.
or is serum protein and albumin measured in a liver function test strictly an indication of nutritional state?
Serum protein and albumin can be used in evaluating
nutritional status, but also as a direct indication of
liver function.  The liver has to be significantly
damaged (in cirrhosis) before you begin to see
decreased albumin levels.

Sure hope things work out for your Mom.