All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
There is no doubt that getting to know that young man through the Internet and communicating with him is immoral and a cause that leads to evil and corruption. You have to repent to Allah from that and cut off your relationship with him completely. You should beware of temptation and its causes, and you should preserve your religion and honor.
With regard to a woman calling a man to goodness – although it is permissible in principle – it involves some prohibitions. Therefore, it is more appropriate to direct him to any reliable and trustworthy Islamic organization or authority so that they would teach him the religion of Islam. If he is interested in Islam, he would endeavor to look for this himself. He may also make use and benefit from our site; we have many fatwas that introduce the religion of Islam, such as the following ones: 86091, 88906 and 173389.
If we presume that he embraces Islam and adheres to the rituals of the religion, especially the prayer, then there is no harm on you to accept him as a husband. Please refer to fatwas 17897 and 11716. However, we have to warn you that some men may pretend to enter Islam in order to achieve their desire to marry a specific woman, and once he achieves what he wishes, then his truth is revealed and bad consequences follow. Moreover, the difference of customs, traditions, and cultures, because of different countries, may be an obstacle to the continuity of the marriage.
Therefore, it is better for a Muslim woman to look for a righteous man who is religious, has a good moral conduct, and whom she aspires to be happy with, especially given that marital life is a long journey that may not be free of obstacles that require reason and wisdom to deal with.
A man asked Al-Hasan Al-Basri, “To whom shall I marry my daughter?” He replied, “To the one who fears Allah, because if he loves her, he will honor her, and if he hates her, he will not be unjust to her.”
Finally, we do not know what you mean by saying, "Am I allowed to be part of that family?" If by this you mean residing with them and so on, then there is nothing wrong with that, provided that you feel safe with them and provided that you abide by the Islamic conditions in dealing with them, but it may be difficult to do so. Of course, all this is if we presume that he has become Muslim.
To conclude, our advice to you is to cut any kind of relationship with that man and not be attached to him and look for a righteous Muslim man to marry. A Muslim woman is Islamically permitted to look for a husband within the limits of the Shariah, as we have already highlighted in fatwa 82471.
Allah knows best.