My son says Regulus was a Death Eater, killed when he wanted to get out. Now we have some connection to Gryffindor...the only relic left associated with Godric is the sword in DD's office, right?
As far as we know, that is correct. I do remember Sirius saying that he didn't think Regulus was important enough to be killed by Voldermort himself. I want to say that Sirius said that something frightened Regulus, but by then it was too late to get out and that is why he was killed. I don't have my books handy, so I will have to check it out a little later.
Correct. It is in his office.
I just reread the passage in OOTP about Regulus. Sirius says the Regulus got scared and was killed by Voldemort. Then he says it was more likely on Voldemort's orders, as Regulus was probably not important enough. However, if Voldemort did find out that Regulus did something with the horcrux or just plain thought about turning against him, Voldemort wouldn't confide that to the Death Eaters. He would tell them that Regulus got scared, tried to quit so Regulus had to be killed. JKR doesn't elaborate on the hows and whys of Regulus' death. Maybe the heart of the lion came out in his actions of the horcrux.