Is it permissible to transfer money from a non-Muslim country via interest-based banks, especially in two cases: the first involving receiving the amount in dollars, and the second involving receiving it in local currency after converting it to a bank account?

There is no harm in the issue of transferring money through banks or exchange offices and paying a fee for the service. For those who find no other means but usurious banks for this purpose, there is no harm in dealing with them for transferring and safeguarding their money, provided they limit it to what is necessary, because Muslims in the West often find no other alternative.