Statement I: Incorrect — Plant ash does not include carbon, as carbon gets oxidized and released as CO$_2$ during combustion.
Statement II: Correct — In amino acids, the amino group and acidic group attached to the same $\alpha$-carbon make it an $\alpha$-amino acid.
Statement III: Correct — Glycerol has 3 hydroxyl (-OH) groups.
Statement IV: Correct — Acid insoluble fractions are generally large-sized macromolecules like proteins, polysaccharides, etc.