Someone else mentioned in another comment how the anime shows them purposefully dying. I agree and think that Vincent and Rachel knew they were plotted against, and died purposefully for something they started. I can see it appeasing some enemy. In that respect, Vincent committed suicide since he just stood there and burned...
No, no, he's a runaway. Grell and Ronald were surprised when they saw his death scythe, because it's against their rules to have one not being on duty, so he probably flew with it. Also, I guess forgiven souls would go to rest, they wouldn't stay around anymore (if they did there would be an infinite number of shinigami, since they'd be all the people who suicided through history).
The thing is what reasons would he have to run away and hide as a human undertaker? Something important must have happened for him to do so (the german shinigami said so, only shinigami who are really tired or the ones who have a very good reason leave their job) (๑•ㅂ•)و✧
Everyone one is suspecting the body double theory but I'm with Ciel. Why would she tell us how shinigami were made if we weren't to see a new one? Maybe Vincent (bless his handsome soul) is a shinigami...