Is a woman`s neck an Awrah (private part)?
All Perfect Praise is due to The Lord of The Worlds.
It is an Awrah, and it is forbidden for her to reveal it before non-Mahrams (Marriageable men). And Allah Knows Best.
I`m married to an American citizen who used to be married to a man in Mexico and filed for divorce there. It is worth pointing that in America she isn`t registered as married. When she arrived in Jordan, her lawyer called and told her that she got the divorce, and based on this we got married in Jordan. What is the ruling of Sharia on this?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
You haven`t mentioned whether this woman has converted to Islam or not. If she had embraced Islam and three menstrual cycles passed, but her first husband hasn`t converted to Islam, then her relationship with him is over. If you married her after this (Passing of three menstrual cycles and first husband not having embraced Islam) then your marriage is valid. However, if she didn`t convert to Islam then your marriage contract with her is invalid and you have to wait until she gets divorced by her first husband and observes Iddah, which is three menstrual cycles. Afterwards, you can conclude the marriage contract. We pray that Allah doesn`t hold you to account for what you have done because you thought she was divorced. We recommend that you seek Allah`s forgiveness as much as you can and do righteous deeds. We also advise you to marry a Muslim woman to preserve your and your children`s religion since Almighty Allah Says (What means): "Wed not idolatresses till they believe…" [Al-Baqarah/ 221]. It is true that marrying a Kitabi (One who believes in a book of sacred scriptures and with whom a Muslim may marry in what is deemed a lawful marriage) is permissible, it involves great risks, as stated in the aforementioned verse. And Allah The Almighty Knows Best.
Does the time of Fajr (dawn) prayer start after the first Athaan (call for prayer), or the second one?
All perfect praise be to Allah,The Lord of The Worlds The time of Fajr prayer starts after the second Adhan. And Allah Knows Best.
A woman used contraceptive pills, and her menses exceeded (15) days, is it permissible for her to fast?
The maximum of menstrual blood is (15) days, but if it exceeded that due to a medication, or the like, then it is Istihadah (bleeding outside the monthly period), and in this case she should perform Ghusl (ritual bath), pray, and fast. Moreover, she is obliged to make up for the missed fasting days which exceeded her regular menses. And Allah Knows Best.
