I have been searching for my problem online for many weeks, but I could not find anything related to it. That is why I am posting a new thread. As far as I have searched, I came to the conclusion that fornication only includes the willful penetration of the female private part by the male one. I have a girlfriend, and we had it decided among ourselves that we would do anything but real sex. So, recently, when we were together, we were naked and I was laying on her. I was rubbing my private part onto her, as we had done a couple of times before, but then it suddenly slipped and penetrated her though none of us had the previous intention of doing that, and I also immediately pulled out. So please tell me with the help of some authentic references whether I thus fornicated or not, as fornication is related to willful penetration, and given that it was by mistake, does this act constitute fornication? Also, please tell me if anal sex falls under fornication or not?

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. 

The Zina (adultery/fornication) that necessitates the Hadd (i.e. the corporal punishment determined by the Islamic Law) is that in which there is complete penetration, but as for what is lesser than this, such as touching, kissing, hugging, and foreplay without penetration, then this does not entail Hadd, but it is still Zina, as the Prophet said, "Allah has decreed upon the son of Adam his share of Zina, and he will inevitably commit it. The Zina of the eyes is by gazing, the Zina of the ears is by listening, the Zina of the tongue is by talking, and the heart desires and wishes. Then, the private parts either submit to this or deny it." [Al-Bukhaari and Muslim]

Another narration reported by Imaam Ahmad has the following addition: "...the Zina of the hands is by touching; the Zina of the feet is by walking [to forbidden places]; and the Zina of the mouth is by kissing..."

The Zina that necessitates the Islamic Hadd is defined by Imaam An-Nawawi as follows in Rawdh At-Taalibeen, "The criterion of the Zina that requires Hadd is the penetration of the glans (the top of the penis) in a forbidden vagina that is desired naturally and about which there is no doubt; this necessities the Hadd."

Ibn Qudaamah said in Al-Mughni, "There is no difference of opinion among the scholars about the fact that whoever has sexual intercourse with a woman in her vagina while she is unlawful for him, and without doubting that she might be lawful for him, has committed Zina, and the Hadd of Zina is obligatory on him if its conditions are complete."

It is a condition for Zina to be confirmed that the top of the penis penetrates the vagina deliberately, such that the person did not mistake another woman to be his wife, nor is ignorant of the prohibition of Zina due to being a new Muslim, nor due to forgetfully having intercourse with a woman who used to be his wife and he forgot that he had divorced her, for example.

Ad-Dardeer says in his commentary on Mukhtasar Khaleel al-Maaliki, "'Deliberately' excludes the one who made a mistake, the ignorant, and the one who forgot, such as the one who forgot having divorced his wife."

Ad-Dusooqi said in his Haashiyah:

"His saying 'excludes the one who made a mistake' refers to the one who intended (to have intercourse with) his wife but made a mistake and had intercourse with another woman. His saying 'the ignorant' refers to the one who believed that she was his wife or a slave girl whom his right hand possessed and then it turned out that she was a non-Mahram (marriageable/alien) woman to him. And 'the ignorant' is also the one who believes that it is lawful to have intercourse with non-Mahram women because of being a new Muslim who came from a land that is remote from the land of Islam." 

It is clear from the above that you deliberately committed the sin of Zina, so you have to hasten to repent to Allah and stop this relationship with a woman who is unlawful for you and seek the forgiveness of Allah as much as you can.

In addition, penetration from the anus (anal sex) is considered Zina.

Ibn Qudaamah, when commenting on his statement on the definition of Zina, said, "Having anal sex is like Zina because it is having intercourse with a woman who is not lawful to him and about whom he has no doubt that she is lawful for him [i.e. she is neither his wife nor a woman whom his right hand possesses]; so it is Zina, like having vaginal intercourse, as Allah says (what means): {Those who commit Faahishah (immorality/Zina) of your women.} [Quran 4:15]. Allah says about the people of Loot (who committed sodomy): {Do you commit such Faahishah...} [Quran 7:80]; referring to anal sex (with other men) as Faahishah." [Al-Mughni]

Allah knows best.