Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
Is the Aqeeqa due on the newborn in case of dying almost a month after the delivery?
Offering Aqeeqa after a week of a newborn death is recommended.
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 Zakah (obligatory charity) due on land intended for selling?
Yes, lands intended for trade are valued, and Zakah is paid according to their estimated value after a lunar year had lapsed, but if the owner didn`t pay the due Zakah, then he should do so after selling them.