Is it more appropriate for a student of knowledge, or a Friday preacher, or a judge, or the imam of a mosque to wear the iqal on his head in these situations, or not to wear it, and why?

Wearing the 'iqal (headband) is permissible, and it is better to follow the custom of the country. If the custom in your country is that the people of knowledge (religious scholars) do not wear it, then it is better not to wear it. However, there is no harm for whoever wears it. The basic principle regarding clothing is permissibility, unless there is evidence that indicates its prohibition.