Is it permissible for a woman to visit the doctor while in her `Iddah (waiting period)?
It is permissible for her to do that during day time, but it is impermissible for her to leave her house at night except for a sound reason. And Allah Knows Best.
Should a woman who broke her fast because of delivery make up for missed fasting days before the next Ramadhaan, and what is the expiation due on her in case she delayed making up for them ?
She should make up for missed fasting days before the start of next Ramadan if possible, but if she didn`t while being able to, then she is obliged to make up for them along with feeding a needy person for each delayed day of the missed fasting days. However, if she wasn`t able to make up for the missed fasting days before the start of next Ramadan, she has to fast a day for every day that she missed, and no ransom is due on her. And Allah Knows Best.
Should Al-Basmalah (i.e. saying Bismillaaahi Ar-Rahmaani Ar-Raheemi) be recited after Takbeerat Al-Ihram (saying Allahuakbar) which marks the beginning of prayer?
All perfect praise be to Allah,The Lord of The Worlds A praying person is obliged to recite Al-Basmalah at the beginning of Chapter Al-Faatihah, and in every Rak`ah (unit of prayer) because it is a verse of it. And Allah Knows Best.
Is everyone obligated to follow the fatwas of his country, and if we adopt the fatwas of scholars of other countries, is it considered a sin?
All perfect praise be to Allah, The Lord of The Wolrds and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.
It is permissible for the person who isn't specialized in Sharia sciences to apply the opinions of renowned scholars whom he trusts ,whether they be from his own country or not ,but if the scholars have different opnions regarding a certain issue/matter, then he must consult someone who is more knowledgeable than himself .It is preferable that you (the questioner) specify the case of your interest ,so that we could give you a more specific answer since some scholars deliver fatwas based on illogical/atypical opinions which should not be applied no matter what .And Allah The Exalted Knows Best.