Is it permissible to engage in commercial transactions with non-Muslims on credit, with them taking a 10% shipping fee of the merchandise price, and settling the amount after two or three months without any increase in the prescribed service fee?

It is permissible to engage in buying and selling with disbelievers. Scholars have based this on the actions of the Prophet, peace and blessings be upon him, and his companions, as narrated in Al-Bukhari from Aisha, may Allah be pleased with her: "The Messenger of Allah, peace and blessings be upon him, passed away while his shield was mortgaged to a Jew for thirty sa's of barley."

Allah has commanded fulfilling contracts, paying debts, and returning trusts, and has deemed the delay of a rich person as oppression. Therefore, a Muslim must render the rights of those non-Muslims with whom he has dealt, and it is not permissible to unlawfully consume their wealth. Muslims are most deserving of fulfilling trusts and honoring contracts.

As for the amount expressed as ten percent, it does not affect the permissibility of the transaction. It is permissible, whether it is for shipping services or a share of the profit.