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.

Is an elderly or chronically ill person required to pay additional fidyah if they delay it beyond the first year?

Is it permissible for a wife to give her money to her family as a charity, or a gift without asking her husband, or seeking his consent?

The wife has the right to give her money as a charity, or a gift to her family, or to other people after consulting her husband out of respect, and this is the meaning of treating on footing of kindness and equity. Therefore, if he wanted to stop her from helping her family, then there is no harm in not telling him.

What should someone do if they fasted for 30 days in their country, then traveled to a place where people are still fasting?

If a person completes 30 days of fasting in their country and then travels to another country where people are still fasting, they should continue fasting with them until they observe Eid. Even if they have already completed 30 days, he/she should abstain from eating and drinking and join the people of that country because he/she has now become part of that community.