Is it permissible for a man to propose to two women and inform each one about the other, and is it lawful for him to take a second wife, even though the first wife has no defect, for the purpose of protecting her and providing for her?

There is no harm for a man in marrying a second wife, even if his first wife is in the best of conditions, for Allah Almighty says: "then marry those that please you of [other] women, two or three or four." Similarly, there is no harm for him in proposing to two women at the same time. He is not obligated by شرع (Islamic law) to inform the prospective wives of this, but it is forbidden for him to lie if asked about it.