What is the ruling on the cessation of blood after (40) days from delivery, but later continued sporadically during two days of Ramadan?

Once postpartum bleeding (Nifas) ceases, and the woman is certain that it won`t reoccur, then she becomes ritually pure and so she is free to make Ghusl (purificatory bath), pray, and fast. If the bleeding reoccurs before fifteen days from its cessation, and before the end of (60) days after delivery, then the ruling on postpartum bleeding is effective, and her fasting and prayer are null and void, thus she must make up the fasting that she missed and not the prayer during those particular days.

What is the ruling on a person who isn`t able to fast due to old age, or an incurable disease?

Paying the ransom is due on such a person, and that is giving a Mud (600 grams) of wheat, or rice, or the price of that amount to a needy Muslim for each missed fasting day. And Allah Knows Best.

When Iddah is Initiated for Deceased's Wife?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Iddah is observed on the same date at which her husband passed away for four months, but as for the pregnant, it is observed at the date she gives birth. And Allah Knows Best. 

Is it permissible for a menopausal woman who has blood discharges to fast?

If she reached the age of menopause, and her menses stopped, but later she saw blood discharges that lasted a complete day and night (24) hours, then it is menstrual blood. Still, if these blood discharges lasted less than a complete day and night (24) hours, then it is not menstrual blood, but it is bleeding outside the monthly period (Istihadah), and it does not prevent her from prayer and fast, but she has to make ablution for every prayer.