Why didn't Regulus at least find out how to destroy horcruxes before he set out to the cave knowing he had to die? It doesn't make sense that he would hunt a horcrux down but not try and find out how to destroy them.
Why also didn't he just decide to live long enough to see the locket be destroyed? He could have lived longer had he either; got Kreacher to dissaparate him (using house elf magic) after he drank the water, learned how fight inferi [with fire as Dumbledore explained] and then with Kreacher supporting him, go back by boat to the entrance and then get dissaperated back to Grimmauld Place once outside.
If he believed there was only one horcrux, why couldn't he have drank the potion, see the horcrux be destroyed and then believing that Voldemort was Mortal now, try and bump him off? [Offcourse with the other horcruxes unkown to him he would have failed]