The reason the fuqahā’ mention to wait for a period of 6 months before one starts to count the ʿiddah by lunar months, is to ensure that the woman in not pregnant. They say that by that semester it would have been clearly visible if she was pregnant. So, 6 months for istibrā’ and 3 months for ʿiddah.

If the woman was divorced on the 1st of the month, then all agree that she will count her 3 months by the sighting of the crescent (hilāl). Therefore, her ʿiddah can be 90, 89, or 88 days.

If she was divorced on any other day, then there is a difference of opinion regarding how to calculate the 3 lunar months

In the chapter on ʿiddah, ʿAllāmah Haṣkafī and ʿAllāmah Shāmī mentioned an exception to the rule of 55 years being the age of menopause. 
If a woman became bāligh by age, i.e., by passing 15 lunar years of her life, and never saw a single ḥayḍ her entire life and she reaches the age of thirty (30), the judgment of being a woman in menopause would be issued for her.

Ḥayḍ terminates when a woman reaches the age of menopause.
Age of “losing hope” for Ḥayḍ and Nifās (i.e., Menopausal Age)

Lunar: 55 years. [Preferred Opinion]
Solar: 53 years 4 months.
Rule 1: When a woman reaches the age of 55 and her bleeding stops, the judgement of her being in menopause is passed.
Rule 2: The ʿiddah (for a divorce) of a woman who reaches the age of 55 and is no longer seeing blood is counted as 3 lunar months.

The Definition of Ḥayḍ
Literal Definition:  To flow.
Sharʿī Definition:
It is a state of ritual impurity. Ḥayḍ is a legal obstacle which prevents a woman from fulfilling such acts of worship which require ṭahārah (purity), such as: Ṣalāh, recitation of the Qur’ān, fasting, entering the Majid, sexual Intercourse, etc.

It is a physical impurity. Ḥayḍ is blood which flows from the [woman’s] womb and exits from the farj dākhil (vaginal opening), even if it is legal (ḥukman) blood without childbirth.

Through the infinite grace and assistance from Allāh Taʿālā alone, He  has granted us the tawfīq to begin this task of sharing important information and masā’il regarding menses (Ḥayḍ), dysfunctional uterine bleeding (Istiḥāḍah) and lochia (Nifās) mainly sourced from “Manhal al Wāridīn”, ʿAllāmah Ibn ʿĀbidīn al-Shāmī’s رحمه الله commentary on Imām Birgivī’s رحمه الله “Dhukhrul Muta’h-hilīn”.

“The validity of many other rulings is based on this such as: ṣalāh, fasting, reading and touching the Qur’ān, iʿtikāf, entering the Masjid, ṭawāf of Ḥajj, puberty, divorce, ʿiddah, permissibility of intercourse, lineage.” [ʿAllāmah Shuranbalālī رحمه الله]

It is considered as one of the most detailed, difficult, precise and intricate topics in the study of fiqh.

In such a case, if blood flows from the womb then the woman will be regarded to be in nifaas and this blood will be considered the blood of nifaas.

It is permissible to read all types of duas when in the state of haidh, to such an extent, that it is also permissible to read those words of duas which are mentioned in the Quran Karim and Ahadith Tayyinah. 

To type the Holy Quran on a typewriter or computer when in the state of haidh is Makrooh [Tanzihi].

Whilst in an impure state, it is not permissible to touch the noble Quran or any such commentary of the Quran wherein the words of the Quran make up the majority of the book and the words of commentary are less.