1.It would need to first prime me for depression and then somehow convince me that I really should kill myself.
A bit more honesty than Metus, I appreciate it.
Depression isn't strictly necessary though (although it helps), a general negative outlook on the future should suffice and the AGI could conceivably leverage it for its own aims. This is my own opinion though, based on my own experience. For some it might not be so easy.
If it's worth saying, but not worth its own post, even in Discussion, it goes here.