Is a man's intercourse with a woman—without a legal contract, witnesses, or a guardian—considered adultery if seminal fluid is ejaculated into the female organ without full penetration of the male organ? Is their marriage considered valid, and does their separation necessitate a divorce?

What happened between your friend and this man is a heinous evil and a clear sin. It is considered zina (fornication/adultery) in the general sense if it was limited to ejaculation without penetration. If there was penetration of the glans into the vagina, then it is zina that necessitates a hadd punishment.

There is no need for divorce here because a valid Islamic marriage did not originally take place. Your friend must repent immediately and cut off her relationship with this man because he is a stranger to her. If their repentance is sincere, then there is no impediment to their marriage if they fulfill the legal pillars of an Islamic marriage.