Becoz if they leave them, their brothers will use them.
all Sikh men have the last name: singh which means lion.
Sikh history is one which has been made by both men and women. There are many, many outstanding Sikh women. The Gurus' wives led highly spiritual and independent lives. Mata Sundri ji led the Sikhs for a long period after Guru Gobind Singh returned to his heavenly home. Sada Kaur was a famous Sikh Jathedar and ally of Ranjit Singh who made possible the Sikh empire of the 19th Century. The list of important Sikh women is endless.
Kaur is a middle name used by Sikh women as in Singh is for Sikh men.
some men cover their hair with a "paag"
Simple answer - Guilt. They know what they did was wrong, they feel guilty and childish. As they should do for breaking their wife's heart.
There is no such thing as a "SIKH necklace" that is mandated by the religion. Some men and women do wear a necklace with the Sikh insignia but it is not required by their faith.
Sikh women can keep their hair long to show they are Sikh and by choice they can also wear a Patka. They can also wear Sikh symbols such as the Khanda, Khesh, Kirpan, etc.
Yes they can
The Sikh religion.
Sikhism has no official doctrine about homosexuality, and most Sikh men follow the universal goal of Sikhism to hate nobody. But there are some Sikhs who condemn homosexuality.
usually women on left and men on right
A Sikh woman has equal rights to a Sikh man. No post in Sikhism is reserved solely for men. A woman is not considered subordinate to a man. Sikh baptism (Amrit ceremony) is open to both sexes. The Khalsa nation is made up equally of men and women. A Sikh woman has the right to become a Granthi, Ragi, one of the Panj Pyare (5 beloved), etc.