Using the OP’s system, Option 2 sounded to me like the right kind of definition, just not exactly the best one. Option 3 includes Christians, but not distinctly. It also includes Zoroastrians & Muslims. Option 2 is not perfect, but it’s in the vein of how I define the term.
Anthropologically, Christianity is definable as a religious tradition, like Judaism or Taoism. It’s unnecessary to exclude bad Christians from the set of Christians, & I don’t care to define the term by anything relying on a dubious theological reality. That sort of thing leads toward nasty comments about members of other sects.
So I’m defining the term anthropologically, as I one would define “Buddhist,” “Jew,” “Marxist,” or “Utilitarian,” without having to believe in any such thing.
My working definition is roughly as follows:
**The set of Christians comprises those who believe that Jesus of Nazareth was the Christ (Messiah), & that this is meaningful to them personally; & who define membership in his church &/or adherence to his teachings as their primary religious identity.
One may speak more strictly of practicing Christians, who maintain membership in some form of the Church, participate in the Church’s sacraments, & try seriously to live by what they understand to be a Christian morality.
One may speak more loosely of cultural Christians, who come from traditionally Christian societies & are informed by the cultures & mores of such societies.**
That pretty much sums it up.
And yes, some Christians do believe in killing people. Maybe their understanding of Jesus’s teaching is imperfect, but for the purposes of a descriptive definition, they are still Christians.