Example 1, initiative is still with the hero. She is protected from and ignoring Herodias, but the evil side is still 3/3 in terms of what affects her (and the battle). She still has initiative, therefore.
Example 2 is more complicated, because only one hero is ignoring Gold; the other is not ignoring. I have to do more research on this, and more thought, so anyone else's input would be helpful. Basically, the problem is that Jeiel ignores Herodias, but also does not strike Herodias (due to the nature of ignore), but Herodias strikes at your Green hero (which is not protected or ignoring).