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 ruling of Sharia on woman shaking hands with non-Mahram man?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The Messenger of Allah (PBUH) said: "It is better to be stabbed in the head than touch a woman to whom one isn`t related." [Transmitted by Al-Tabarani /Al-Mo`jam Al-Kabir, Hadith No.16880]. Accordingly, it is forbidden for men to shake hands with non-Mahram* woman. And Allah The Almighty Knows Best.
* The women/men that you are allowed to marry. It includes all women/men other than mahram (including cousins).
Is it permissible for a woman whose menses exceeded (15) days to pray, fast and do what was prohibited on her to do during the latter period?
If the menses exceeded 15 days then it is deemed menstruation, and in this case she is obliged to pray and fast and to do what was impermissible for her to do during the latter period. In addition, she is obliged to make an ablution for each obligatory prayer after it's due time and making sure that impuity is removed. Finally, your menstruation period is over (Questioner) simlar to your menstruation in the previos month.
Is it permissible for a wife to boycott (not to attend to his different needs) her husband?
It isn`t permissible for the woman to boycott her husband unless he is the reason behind that, and it is recommended that both spouses seek the advice of righteous people to make reconciliation.