Is it permissible for a Muslim to ask a non-Muslim to transfer a sum of money to him via the bank, and is this considered an act of loyalty to disbelievers or entrusting matters to them?

There is no harm in a Muslim seeking help from a disbeliever in transferring money, even for a fee. This is because the Prophet, peace and blessings be upon him, and his companions used to deal with disbelievers in buying and selling. The Prophet, peace and blessings be upon him, bought food from a Jew on credit and mortgaged his shield. It is permissible to deal with disbelievers in matters where no prohibition on the transaction has been established. This does not fall under the prohibition of al-muwalat (taking them as allies), which refers to the prohibition of allying with them against Muslims, being pleased with their disbelief, imitating them, or loving them.