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 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”.
Is it permissible for a financially capable woman to pay the Zakat to her sons or one of them?
It is permissible for a mother to give her children from zakat if they are eligible to receive it, even though she is obligated to provide for them. This is based on the saying of the Prophet Muhammad (PBUH) regarding Zainab, the wife of Abdullah Ibn Mas'ud (may Allah be pleased with them): "Your husband and your children are more deserving of your charity" [Al-Bukhari]. And Allah Knows Best.
If husband doesn`t pray, but wife does, is their marriage contract considered valid or not?
All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Not observing daily prayers is a grave sin, but doesn`t invalidate a person`s marriage contract. However, we advise you to save your husband from hellfire by convincing him to observe the prescribed prayers. And Allah The Almighty Knows Best.