If it's inheritable wouldn't that make it by definition genetic?
If you inherit a virus from your mother, for instance, I think most would call that non-genetic inheritance, even though viruses have genes too. Same goes for methyl and acetyl markers, transcription factors, nutrients, toxins, and whatever else comes along for the ride in the meiotic cell.
epi- = outside
But there might be other ways that some traits get inherited, eg by changing the cellular environment in the sperm/egg itself which could affect the offspring while keeping the genes the same.
Even the definition of a gene is not very accurate. Many important sequences yield a miRNA or another RNA. Only few sequences yield a mRNA. Some "genes" are just integrated viruses/phages/transposons etc... that were modified. One of the most fascinating one was the retrovirus in regards to the mammalian placenta: https://pmc.ncbi.nlm.nih.gov/articles/PMC4332834/ but there are many more examples. We are all DNA hybrids at the end of the day. The whole species concepts makes very little sense these days, IMO. I can see the use case for eukaryotes, but it makes no sense to me for bacteria yet alone viruses.
It’s a very young field with a lot of open questions. The concept has been adopted and abused in the mainstream so you have to be careful to separate the science from the pseudoscience.
https://en.wikipedia.org/wiki/Epigenetics#Definitions
That depends on the definition. But, if we use the modern definition, it emerged (or re-emerged) in the 1990s. It's not old, indeed, but I also would no longer call it "very young". It's soon 40 years in the modern definition, and much older if we include prior discussions.
E.g., I would regard computer science as a very young field.