“I don’t think Christians who are not of Jewish origin can convert to Judaism, at least not to Orthodox Judaism, imho”
You are incorrect. I personally know scores of people who were observant Christians who have formally converted to Orthodox Judaism, having studied for several years with an orthodox rabbi to do so. In fact, those who do the most deep thinking about why they want to leave Christianity and convert to Judaism choose Orthodox Judaism. Some actually converted first to Conservative or Reform Judaism and realized once in those movements that there was so much missing there that they underwent another conversion in an orthodox setting.
It is my understanding that your mother must be Jewish for you to be considered Jewish.
If you’re not Jewish upon birth, you cannot become a Jew. You are considered a Jewish convert. Provided that you marry a Jewish woman, you’re children would become Jewish.