What should a person who was favored from Allah with a newborn, but couldn`t afford an Aqeeqah, do?
Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth) is a desirable Sunnah for the financially able since Allah, The Exalted, charges not a soul beyond its capacity. Therefore, if the father couldn`t afford the Aqeeqah before the end of his wife`s confinement, then it isn`t due on him, and if he was able to afford it later on, then it is permissible, but if he didn`t until the child reached puberty, the latter can offer the Aqeeqah himself.
Is it permissible for a woman whose menses exceeded (15) days to pray, fast and do what was prohibited on her to do during the latter period?
If the menses exceeded 15 days then it is deemed menstruation, and in this case she is obliged to pray and fast and to do what was impermissible for her to do during the latter period. In addition, she is obliged to make an ablution for each obligatory prayer after it's due time and making sure that impuity is removed. Finally, your menstruation period is over (Questioner) simlar to your menstruation in the previos month.
Does fasting on behalf of a deceased person permissible?
Fasting on belhaf of a deceased person is permissible, since the Prophet (PBUH) said: "Whoever dies while he still has some fasts to make up (of the days of Ramadan), then his heir (any of them) should fast on his behalf." [Agreed upon]. The previous answer is for making up missed obligatory fasts on behalf of the deceased. But if the fasting on behlaf of the deceased was for performing a voluntary acts of devotion such as fasting....is permissible as adopted by the majority of Muslim scholars and based on the above hadith as they stated "Every good dead intended to be on behalf of the deceased its reward will reach the latter." And Allah Knows Best.
Is buying shared land from someone who has taken possession of it considered halal or haram?
The shared land is possessed by the country i.e. for all people; therefore, it shouldn't be possessed/occupied save by it's guardian/owner permission,thusly it can't be possessed save by having owners' permission. Finally, buying it from a person who don't possess it is impermissible. And Allah Knows Best.