Is permissible to buy/sell with non-Muslim?
Yes buying/selling for a Muslim with non-Muslim is permissible as regards what is lawful.
Is Zakah (obligatory charity) due on leased property, and how is it calculated?
Zakah isn`t due on the leased property itself, but on the saved income from that property if it reached Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over saving it.
Are all the children of a suckling woman considered brothers to the strange child whom their mother had breastfed, or just to the one who had suckled with him?
All the children of the woman who had suckled a strange child are considered his/her brothers and sisters.
Is it permissible for me to name my newborn baby boy “Al-Moustafa” ?
There is no harm in naming your son “Moustafa” without using the ”Al”.