Is the maternal uncle of one`s mother a Maharam?
All perfect praise be to Allah the Lord of The Worlds. May His blessings and peace be upon our Prophet Mohammad and upon all his family and companions.
Mother`s maternal uncle is a mahram. And Allah The Almighty Knows Best.
* In Islam, a mahram is a member of one's family with whom marriage would be considered haram, concealment purdah, or concealment of the body with hijab, is not obligatory; and with whom, if he is an adult male, she may be escorted during a journey, although an escort may not be obligatory.
Is it permissible for someone to make a supplication to Allah to marry an already married, or an engaged woman?
No, it isn`t, and the person who does so is sinful before Allah, The Almighty.
Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
Is it permissible to recite the Holy Qur'an or to play a recording at mourning gatherings? Or is it considered an innovation?
Whenever Qur'anic verses are recited, it is obligatory upon everyone to listen, otherwise; they should remain silent. And Allah Knows Best.