How Are The 3 Lunar Months Counted 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:

Menopause at 30 Years of Age: An Exception

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.

Menopause Rulings

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.