I made a vow "If the Israeli troops retreated out of Gaza strip I will buy a cake from a certain bakery" and it happened. Am I obliged to buy from the same bakery?
You are obliged to buy from the same bakery. And Allah Knows Best.
My husband told me that he concluded our marriage with a fake name that belongs to another person, because he was sentenced. Nowadays, he brought an ID, passport and birth certificate with the his current name. What is the ruling on being married to him?
praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
As regards being married to the person mentioned in your question: The marriage is valid so long as he was the same person your guardian concluded the marriage with, even if he changed his name i.e. if your marriage contract was concluded with the same person, since what counts regarding marriage is the persons not names. And Allah Knows Best.
A person vowed to slaughter a sacrificial animal. Is he permitted to eat from it?
If the vowed sacrificial animal was for the sake of Allah, and the one who vowed didn't specify then its meat should be distributed only among the poor and needy similar to distributing Zakah of Al-Fiter so neither him nor his dependents permitted to eat from; however if his vow was to made a banquet and invititing his relatives and others; then he must bring up as much as he can from its meat for them. In addition, he is permitted to eat from it in a reasonable basis. And Allah Knows Best.
Is it permissible for a person who has to make up for missed fasts to fast six days of Shawal (the month directly after Ramadan) before making up for the missed fasts ?
Yes, it is permissible for him/her to do so, but it is better that they make up for missed fasts first. And Allah Knows Best.