Am I sinful for the suicide of a non-Muslim girl I met online, who loved me without seeing me, and whom I did not tell about my engagement, knowing that I tried to stop her after I found out and she committed suicide?

It is not permissible to establish a relationship between a man and a woman except under the umbrella of a legitimate marriage. They should not converse unless there is a need, and then with modesty, avoiding anything that could lead to temptation. This is based on the Almighty's saying: ﴿And when you ask [his wives] for something, ask them from behind a partition. That is purer for your hearts and their hearts﴾ [Al-Ahzab: 53], and His saying: ﴿Then do not be soft in speech [to men], lest he in whose heart is disease should covet, but speak with appropriate speech﴾ [Al-Ahzab: 32]. This includes conversations and correspondence over the internet, as they lead to great corruption. Whoever has become involved in such relationships must repent to Allah, especially if it involved lying or making the girl's heart attached with the promise of marriage.