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 buying a car from someone for less than the market price, because they are in a hurry to travel and want to sell their belongings at a lower price due to their urgency?
Yes it is permissible; however, a Muslim shouldn't take advantage of other's difficult situations.
What is the best charity to offer on behalf of the deceased? Is it giving food, reciting Quran, giving money or supplicating? What is the best charity to offer on behalf of dead father and dead husband? What is the best continuous charity to offer on behalf of the deceased?
Praise be to Allah the Lord of the Worlds. The deceased benefits from every righteous deed offered on his/her behalf, be that continuous charity, reciting Quran or a pious son praying for him/her. However, the best righteous deed is performing Haj and Omrah on their behalf especially if he/she hadn`t performed that ritual for it remains a debt on them. The evidence on this is that Ibn 'Abbas (Allah be pleased with them) reported: A man came to the Messenger of Allah (PBUH) and said: "Messenger of Allah, my mother has died (in a state) that she had to observe fasts of a month (of Ramadan). Should I complete (them) on her behalf? Thereupon he (the Holy Prophet) said: Would you not pay the debt if your mother had died (without paying it)? He said: Yes. He (the Holy Prophet) said: The debt of Allah deserves more that it should be paid."{Related by Muslim}. And Allah the Almighty knows best.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.