> I read about the Hongerwinter where kids were born for many generations with health problems.

This is a common misconception. The Dutch famine cohort consists of individuals born during or shortly after the famine (i.e., prenatal exposure to famine). People have shown that these individuals have elevated risk for several metabolic, cardiovascular, and psychiatric disorders (recent review), as well as persistent changes in DNA methylation.

Whether these epigenetic changes can be inherited is rather controversial. There's been some followup (search "transgenerational") in the Dutch cohort indicating some transgenerational effects. However, the effects aren't super strong, and, as far as I can tell, nobody's done the molecular biology to show that these effects are due to genuine epigenetic inheritance, or something more banal like parental or environmental effects.

> [A]re the "mutations" acquired through epigenetics imprinted forever in the genome ... ?

This would violate a lot of what we know of meiosis. Briefly, there's a lot of evidence indicating that chromatin state is wiped and effectively reset during meiosis through to embryogenesis.