Is there any problem for a woman who wears the niqab to submit a copy of her national ID to the person responsible for collecting documents and to the doctor, as this will reveal her face?

If your studies are beneficial to you and your community—in terms of knowledge, practice, da'wah (inviting to Islam), and application—then there is no harm in providing a copy of your national ID card to the officials. You may slightly darken the photo to avoid the clarity of facial features.