Is it permissible to propose to a 17-year-old girl who does not fully cover her face, and is this trait considered influential on her religiosity, and do repeated supplications for a righteous wife suffice over performing Istikhara prayer in this case?

The preponderant opinion is that a woman's entire body is 'awrah (private parts that must be covered), including her face and hands. The view permitting their exposure is bound by conditions that are not met in this era due to the corruption of people. If this girl does not cover her face based on this opinion, then she has deviated from the correct path, but that does not mean she is not committed to her religion. She should be encouraged to cover her face, and it should be explained to her that this is the preponderant and more cautious view. There is no impediment to marrying her, and after marriage, she must obey you in what is right regarding covering her entire body, including her face and hands. Istikhara prayer is required before every matter that a person is concerned about.