Is it permissible for one to give the Zakah(obligatory charity) to his indebted brother?

It is permissible for one to give the Zakah to his indebted , or poor brother.

Is it permissible for a woman to wear colored lenses?

All Perfect Praise is due to Allah, The Lord of The Worlds.

Wearing colored lenses for treatment is permissible, and wearing them as an adornment is also permissible, provided that she isn`t seen while having them on by non-Mahrams (Marriageable men). And Alalh Knows Best.

What is the ruling on swearing a false oath by the Holy Quran?

Swearing a false oath by the Holy Quran dips the oath-taker in Hellfire, and one who had done so should turn to Allah in repentance, seek His forgiveness, give back rights to whom they belong, and pay the oath expiation.

What is the ruling on singing and listening to it while accompanied and unaccompanied by musical instruments?

Singing and listening to it unaccompanied by musical instruments is permissible as long as it isn`t practiced as a profession and is done by a man to other men, or a woman to other women with maintaining that no temptations are involved. The words of the song should be Islamic, and if temptation was likely to happen, then the singing becomes definitely forbidden. Temptation here means: whatever leads to committing a sin. In Islamic Sharia, singing accompanied by musical instruments such as the lute and the like is forbidden, and listening to it as well. The reason behind that is the fact that the musical instrument itself is forbidden. However, striking the tambourine and singing Islamic songs are permissible in weddings, circumcisions and the like.