captain ahab, I'll take a stab at your questions. Yes, you can sell gold coins on ebay. Go take a look there at the current listings, and ... at any given time .... you'll see no shortage of people buying and selling gold coins on ebay. So why would you think for a minute that you "can't sell gold coins" ? And no, no one asks "where did you get this coin?" I mean, sure, they COULD ask you that, but why would they? And even if they did, well .... you inherited it from your dad who was a collector, RIGHT? I mean, people routinely buy/sell/trade/collect gold coins (and coins of all sorts), so why would you think this would be some sort of pressing concern, any-more-so than if you sold a collectable piece of furniture, a used car, a stamp collection, etc... ? No one cares. I mean, the person buying probably doesn't even know you found it with a metal detector anyhow. And even if he did get wind of that, and asks, well... you found it in your back-yard, right? And heck, even if you said it was found in a park, or school yard, or on the beach, etc... ("public land"), since when is that wrong to have found something valuable to begin with? Detectors are a common site on "public land", and since when can you "not find something good/valuable" there? If that were a given, then ... why are those people swinging detectors? Just to get arm exercise ?
As for the "tax" part of your question: Technically, yes. (well ... you asked). Any "income" (when something is turned to cash) technically must be reported on your income tax. No matter how negligable. Ie.: if you're walking down the street and find a dollar, you must report the additional dollar on your tax returns.
Now *realistically* I don't know of anyone who does. If a person made their living treasure-hunting, then I guess a person's conscience might compell him to report his income. But realistically, smaller amounts like this (and baby-sitting income for teenagers, etc..., and the dollar found on the street) is usually considered innocuous and silly to deal with.