Is it permissible for a woman to leave her house wearing brightly colored clothing?
Brightly colored clothing is of woman's adornments, however; and this shouldn't be revealed save to her husband and Mahrams. And Allah Knows Best.
What is the Iddah period upon death of husband? What is the ruling when the woman observing Iddah after death of husband leaves her home to visit relatives although her Iddah hasn`t ended? What is the ruling on her wearing gold during Iddah period?
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.
For a woman whose husband has died, the 'Iddah* is four months and ten days after the death of her husband. If a woman is pregnant, the 'Iddah lasts until she gives birth. Moreover, she has to mourn, not wear gold, perfume nor saffron-colored garment. The evidence on this is that The Prophet (PBUH) said: "It is not lawful for a Muslim woman who believes in Allah and the Last Day to mourn for more than three days, except for her husband, for whom she should mourn for four months and ten days." [Agreed upon]. And Allah The Almighty Knows Best.
*The iddah is a waiting period that a Muslim woman observes after the death of her husband or after a divorce. The Quran says: For those men who die amongst you and leave behind wives, they (the wives) must confine themselves (spend iddah) for four months and ten days.
Is it permissible for a person who hasn`t made ablution to call for prayer (Adhan)?
All perfect praise be to Allah, The Lord of The Worlds. It is disliked for a person with a minor impurity to call for prayer, but if he does , then it`s valid and sufficient. And Allah Knows Best.
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.