Is the salary considered permissible if one transitions to a job that requires attendance one day a month while receiving a full salary, if the employer allows this and requires payments to secure the job?

It is permissible to transfer to a new job, or to work a little after transferring, provided that this does not violate labor laws and regulations. It is permissible to pay money to obtain a right if there is administrative corruption preventing it. Other than that, it is not permissible to pay money because it is a prohibited bribe.