in effect, both cases are the same as her nikah is batil therefore she will be committing zina in (1) and (2). in case number two it will be kufr only if she denies the hukm that she is not allowed to marry a non-muslim man.
both are classified as adultery/fornication which is a kabirah [an enormity/a major sin]. the woman remains a muslim as long as she acknowledges/accepts that she is committing a sin. Allah ta'ala knows best.
(1) has sex with a non Muslim man (2) marries a non-Muslim man? I am confused because I have heard different answers. Some people say that (1) will make her out of Islam whereas others say that it is a mortal sin but not kufr. Who is correct? (2) I know is also a mortal sin and the marriage will be invalid but will it make that woman a non-Muslim too? Please answer. This question is relevant since a lot of Muslim women (and men) in the West are engaged in such activities.