Hi Ismail -
1. the official line is that a Jew is ALWAY a Jew no matter what they convert to, this would halachically apply to the child of a Jewish women who has converted to some other religion they still remain halachically Jewish all their life.

2. However it seems that biblically Jewish lineage is from the Father thus her children may not be considered Jewish if their father was not.

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Just a side point that is my own opinion, Messianic Jews who are moderately observant Jews (ie. born Jewish) but who happen to believe in Jesus being the Messiah are still Jewish. (it is questionable if they would be accepted in many Orthodox communities though - but mainly because of the historical persecution of the Jewish by the Christian clergy throughout the middle ages)

There are other combinations of Jewish Christians - Hebrew Christians who take on much of Jewish ritual life and even 'convert' to become Jewish in order to become better Christians.