Thank you for your letter in inquiry. It seems that your predicament is a difficult one. Having become involved in a relationship with this girl, you now seem to be attempting to find some basis to legitimize what she feels is inappropriate. I presume that you are not attempting to figure out a way that you can "get around" the sin issue (a problem that has clearly developed through your fantasizing about sex, etc....). Relationships that are influenced by these types of obstacles to purity and respect possess little hope of thriving.
This girl is correct in "putting on the brakes" in your relationship. Scripture clearly speaks of the impropriety of being involved in relationships with people who are not believers (defined as someone whose Christianity cannot help being "practised").
1 John 3:9 is discussing the issue of the inappropriateness of sin in the believer's life. As the article you cited states, vv. 4-6 discuss the incompatibility of sin and the Savior. Sin is a reproach to the name of Christ, in whom "there is no sin." When a person is truly in Christ abiding, there is a practical impact in his life. That impact is that he is ruined as a sinner -- he cannot continue in sin without the Holy Spirit of God producing guilt & shame.
Despite the argument of the article you cited, the use of the term "practices" in the present tense conveys the idea of one's characteristic behavior. In v. 8 we are told that the characteristic behavior of an unbeliever is indulgence in sin (proof of what sphere one is part) but, the believer's characteristic behavior is an abandonment of sinful indulgence - v. 9. The first portion of this chapter clearly teaches that we are not yet fully conformed to the glorious, sinless ../image of Christ Jesus in our practical experience. Positionally, we are conformed since we are fully justified through the blood of Christ. However, regarding our sanctification, there are practical developments that every believer can expect to experience. Consider v. 2-3: "Beloved, now we are children of God, and it has not appeared as yet what we will be. We know that when He appears, we will be like Him, because we will see Him just as He is. And everyone who has this hope fixed on Him purifies himself, just as He is pure."
Your friend's sensitivity to God's Spirit is appropriate. I'd like to urge you to consider your own relationship with Christ. You mention that you are not a "practicing Christian." What is that? This entire discussion is emphasizing the essential impact that being born again has on a person's life. If you are a Christian you cannot help but be "practicing" your faith. Can it ever be said that you are not a practicing human being? Or I'm not a practicing male? Perhaps what really needs to happen is for you to realize the offence that your sin presents to a holy God. Then consider the degree of love that God has already shown to you by staying His wrath for your sin and sending Christ Jesus to receive the punishment for it. Then, place your personal faith in Him to forgive you and cleanse you solely through the blood of a risen Lord and Savior who lives to give life to all who would come to Him in faith.