Zees and Oomis: No, murder B’meizid gets Misas Beis Din. There is a Machlokes Tannaim whether the Go’el Hadam killing the Rotzeach is a R’shus or a Chiyuv.
Akuperma: You are wrong on three counts.
1. Giluy Arayos can happen anytime, though any Yeihareg V’al Ya’avor case is incredibly rare nowadays. In face, nowadays Giluy Arayos cases are probably the most common cases of Yeihareg V’al Ya’avor, though I won’t explain why.
2. A”Z is always Yeihareg V’al Ya’avor, whether in public or in private. There is no distinction. The way you said it makes it sounds like there is potential room for the Halachah to be different in private. There isn’t.
3. Performing an abortion would not be Yeihareg V’al Ya’avor according to almost all of the major Poskim aside from R’ Moshe.