Is it permissible for me to consider a girl who is not a relative of mine as a sister in Islam, and to speak with her and look at her face, knowing that our relationship is limited to discussing religion and encouraging each other to perform acts of obedience?

Whoever thinks that the corruption of the times permits him to fall into sins is mistaken. Satan strives to portray sin in the guise of obedience and exploits people’s heedlessness and ignorance, as evidenced by the verse: "He said, 'Because You have put me in error, I will surely sit in wait for them on Your straight path. Then I will come to them from before them and from behind them and on their right and on their left, and You will not find most of them grateful.'" The Sharia has forbidden free mixing, seclusion (khalwa), looking, and handshaking between men and women to prevent means to corruption, as the Prophet (peace be upon him) said: "No man is alone with a woman but the third of them is Satan." Friendship between the sexes is considered among the greatest prohibitions and a means to temptation, and looking at the face of a non-mahram woman is forbidden. Therefore, this relationship must be decisively dealt with, either by marrying the righteous girl if one is capable, or by severing the relationship entirely, as it is a door to evil and corruption.