What is the best manner in distributing the meat of the Aqeeqah?
It is better to divide all of it as cooked meat amongst the poor and the needy. Dividing it into three portions is a Sunnah, but it is permissible to keep all of it provided that a portion, even a small one, is given to the poor and needy(one kilo for example).
Is it permissible for a woman to swear a false oath by the Holy Quran to please her distrustful husband?
It is forbidden for a person to do so since this is considered a false oath(Yamaan Ghamoos) which dips(Yaghmos) its taker in Hellfire if he/she doesn`t seek repentance, and he/she has to expiate for that oath. You should avoid any doubtful acts so that your husband`s chest remains clear from the evil suggestions of the devil.
Are minors(persons under the age of puberty) obliged to fast?
A male under the age of puberty isn`t required to fast, but his guardian should order him to fast if he was able to endure the hardship until he gets used to it.
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.