A neutral/neutral character isn't limited to Nexus, they can also join Outlander or Herald. Assassins are difficult to fit in Outlander, however.

In theory you could also join Battle, but they are unlikely to be able to accept you if you ever drank a potion in your life.

Herald is your best bet, and you can PK anyone you want as long as you have a reason to do it (explore ideas about what your character hates, or make friends and then help them fight their enemies).

Alignment change: don't. Lots of people will take your "betrayal" as an excuse to kill you, and you will get an extra bad vuln to divine power and probably lose some of your skills too.

On edges: see "help edgepoint specifics". But I wouldn't advise counting on getting many edges. 20-25 used to be the norm for long-lived characters, then the ways to get them were gradually removed, but some of the current characters from the Fifth Age might still have 10+ edges.