I think when a single ship is destroyed, it shouldn't make a ship graveyard, but if an entire fleet is wiped out plus a few ships destroyed from the other fleet, then, you have a ship graveyard.
And if a graveyard shows up, you can get bonuses from it with a survey module on one of your ships.
a. A Precursor ship (I mean a real Precursor ship, organic and everything. A Dread Lord ship/A Arnor ship)
I doubt that the race that got blown up would have that kind of technology, by getting a free enemy ship that was blown up in the battle would be useful. If they had that kind of technology, YOU would be the one blowing up.
b. Parts for a ship (Improve either Military Production, Weapons, or Speed?)
good idea, if you dismantle some of the parts on their ships, you may find some useful stuff, for instance, if they have warpdrive IV engine (and you haven't gone up that far on the propulsion tech tree branch yet) you could receive that tech for free.
c. Information from a ship's databanks (Cuts time required to research a tech/grants you a tech?)
This will fall under the explanation for "b". I doubt that they will leave such important info on board a ship that may likely die. In world war two the US kept it's secret code books only on naval vessals, because they would sink and the books would be lost for ever (they made the books out of lead in the navy). BUT, if you interogate a surviving crew member, you could get info on military installations, and where important fleets are positioned.
And if there is nothing of value to you in the graveyard, you could just give all the stuff to a weaker ally, or sell it all to pirates!