What is the ruling on throwing a paper with "Ramadan" written on it into the trash, given that this is not considered a mockery of the holy month? And what is the ruling on throwing a paper with "Jerusalem" or "Medina" written on it?

The preponderant view is that the Arabic letter itself does not possess sanctity unless it contains something venerated by Islamic law, such as the names of Allah or the prophets. Therefore, there is no sin upon one who discards letters that do not contain religiously venerated elements. Some scholars held the view that the Arabic letter should be respected absolutely, but the preponderant view is that there is no sanctity. As long as the doer did not intend to mock Ramadan, there is no sin upon him. It is better not to degrade the Arabic letter to avoid scholarly dispute. As for discarding something upon which is written "Madinah" for example, it is disliked as a tanzih (dislike of avoidance) due to its status, but there is no sin in discarding it, Allah Almighty willing.