Has the Hebrew word for an "idol" been clearly defined as to what is an Idol and what is not?
Yes it is defined but as often occurs in Jewish law, there's a tremendous amount of nuance from case-to-case. But I will simply point out that one can theologically violate "worshipping something other than God" without necessary rendering a specific object an "idol." (E.g. if someone walks onto my yard and bows down to my apple tree and tries to worship it, he is committing idolatry, but he had no ownership of my tree and therefore didn't render it an "idol." I can still use that tree. Versus a tree that was planted for the purposes of worship is prohibited from use.)
The Talmud's tractate of "Avoda Zarah" (foreign worship) devotes its third chapter to this, what's called an idol and what's more likely a decoration. E.g. a rule of thumb had been that a Greek/Roman statue of a person holding a globe, staff, or bird was likely actually idolized, whereas a statue of a person holding something else (e.g. a torch?) was probably just symbolic. Similarly there's the story of a Greek bathhouse with an image of Aphrodite on it; a rabbi still used the bathhouse. Asked how he could do so, he explained (after exiting the bathhouse, as we don't discuss Torah in a bathhouse): "you Greeks didn't say, let's build a bathhouse to glorify Aphrodite. You said, let's build a bathhouse because we want one, and we'll put an Aphrodite on it to glorify the bathhouse!"
Later works such as Shulchan Aruch discuss many more cases (e.g. the Hispanic-products aisle in many supermarkets contains candles with pictures of saints on the glass jar -- while I strongly recommend buying regular candles instead, if this was the only candle available, a rabbi should ask -- was that truly made for the purpose of worship, or was that made by Acme Candle Co. who would just as happily put SpongeBob Squarepants on the jar if it sells better?)