She became mentally ill then she killed herself; is she regarded as having committed suicide?

Praise be to Allah.

Firstly: 

Suicide is a major sin for which Allah warns of a grave punishment. The one who kills himself with something in this world will be punished with it in the Hereafter. See the answer to question no. 70363 

Whatever befalls a Muslim of physical disease, such as cancer, or mental disease such as depression that he cannot bear, that does not make it permissible for him to kill himself. See the answer to question no. 111938 

Secondly: 

A Muslim may be affected by mental or physical illness that affects his mind to such a great extent that he does not know what he is saying or doing. If this results in him killing himself, he will not be with the sinners who have fallen into the major sin of suicide. Rather he will be excused because there was an impediment to his being accountable, namely his loss of reason. 

Based on that, if what happened to your family friend of post-traumatic distress affected her mind, and she did not know what she was saying or doing, then she comes under the ruling on those who are affected by insanity, and she will be excused and not regarded as sinning by having killed herself, because the Pen has been lifted and her bad deeds are not recorded when that is the case. So she is included in the words of the Prophet (blessings and peace of Allah be upon him): “The Pen has been lifted from three: from the sleeper until he awakens, from the child until he reaches puberty and from the insane person until he comes to his senses -- or until he comes round.” Narrated by Abu Dawood (4403), al-Nasaa’i (3432) and Ibn Maajah (2041). Classed as saheeh by Shaykh al-Albaani in Saheeh Abi Dawood. 

In al-Mawsoo‘ah al- Fiqhiyyah (16/99) it says, defining insanity: 

With regard to (fiqhi) terminology, the fuqaha’ and usooliyyeen defined it in various ways, such as: 

It is mental disorder, in such a way that the person cannot do or say things properly, except rarely. 

And it was said that insanity is loss of the ability to distinguish between right and wrong or to recognize their consequences. 

The author of al-Bahr al-Raa’iq defined it as loss of the ability to understand issues from all angles. End quote. 

But if that psychological pressure on your family friend did not affect her mind and it was no more than psychological pressure, and she knew what she was saying and doing at that time, and was able to distinguish between good and bad, and between right and wrong, then she is not excused for killing herself; rather she is accountable for her actions. We ask Allah to forgive her, to comfort her family in their loss and to reward them for it. 

And Allah knows best.