Is it permissible for a female medical student to listen to recorded private lesson tapes and study materials if she does not know whether the owners of these lessons forbid or permit it, and must she ask them herself?

As long as you do not know that the professors prohibit recording lectures, the default is that it is permissible for students to benefit from and disseminate the lectures; because it relates to the spread of knowledge, and there is no sin upon you in doing so. Continue on this default unless you come to know or it becomes highly probable to you that the owners of the lectures have not given permission for their recording, in which case you should refrain.