What is the ruling on continuing to use a personal bank account for simple commercial transactions, due to the inability to open a commercial account, knowing that there is a bank condition prohibiting this?

A Muslim must fulfill the lawful conditions in contracts, based on the general meaning of Allah’s saying: "O you who have believed, fulfill [your] contracts," and the Prophet’s (peace be upon him) saying: "Muslims are bound by their conditions." Therefore, whoever opens an account in a bank must abide by the signed conditions. It is necessary to verify with the bank management whether the transfer operation mentioned in the question indeed falls under the commercial account.