Is the questioner responsible for his children born of adultery, given his desire to return to his country and marry, and is he obliged to inform his future wife about his past?

What happened to you is evidence of the danger of residing in lands of disbelief (Kufr), and it is not permissible for a Muslim to have an unlawful relationship with a foreign woman. This is an act of the جاهلية (pre-Islamic ignorance), and fornication/adultery is a grave sin from which one must repent and sever the relationship with that woman. As for the two children, they are children born of fornication/adultery and are not attributed to you according to the majority of jurists. Therefore, you are not responsible for them. However, some jurists have permitted attributing a child born of fornication/adultery to the fornicator/adulterer if he acknowledges paternity. You should strive to maintain a good relationship with the two children and preserve their religion and morals. You are not obligated to inform your future wife about what has passed; in fact, it is not permissible to inform her, because it is obligatory for a Muslim to conceal his own faults.