Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.
Is it permissible for a woman who has become pure before the end of forty days of confinement to perform different acts of worship? and is it lawful for her husband to have sex with her?
Once postpartum bleeding ceases and she is certain that it won`t happen again, she becomes pure, and so she should perform Ghusl (ritual bath), pray, and fast. She can also have sex with her husband even before the end of (40) days because the minimum of postpartum bleeding is a moment, and the maximum is (60) days. However, the postpartum bleeding for the majority of women is (40) days, but this does not apply to rest of them.
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 it permissible for a Muslim woman to leave her house adorned and without wearing her proper Islamic attire?
A Muslim woman isn't permitted to leave her house adorned and without wearing proper Islamic attire. And Allah Knows Best.