Is it permissible to continue communicating with a girl via the Internet and phone with the intention of marrying her, given her current refusal to get engaged, and is this considered a reprehensible act or permissible as long as the intention is marriage?

There is no doubt that establishing a relationship and conversations with a foreign girl via the internet and then mobile phone is wrong, because such relationships lead to evil and corruption. You must cut off this relationship immediately. If you want to marry her, it is best to meet her without being in seclusion, and to look at her face and hands; as the Prophet, peace and blessings be upon him, said: "If one of you proposes to a woman, and he is able to look at what would induce him to marry her, then let him do so," and "Look at her, for that is more likely to create affection between you." Then propose to her through her guardian. If they agree, it is best for you to solemnize the marriage so that communication becomes permissible for you, and there is no harm in delaying the consummation until she finishes her studies. If they refuse your marriage to her, then stop pursuing it and do not occupy yourself with her.