Is it permissible for a man to marry a second wife and leave her in her country, visiting her annually or every two years? Is it permissible to marry without the first wife's knowledge? And is it permissible to marry with the condition of not being responsible for living expenses?

There is no objection to marrying a second wife if she (the second wife) agrees and waives her rights, such as overnight stay (Qasm) and financial support (Nafaqah). The first wife's knowledge is not a condition, though seeking her permission is preferable to placate her and avoid her anger.