What is the ruling on drawing the cross on paper for study purposes, and is that considered apostasy or merely a sin?

It is not permissible to draw the cross. The Sharia (definition) came to break it and change its form, not to draw it, based on the Hadith (definition) of Aisha (may Allah be pleased with her): "The Prophet (peace and blessings of Allah be upon him) would not leave anything in his house that had crosses on it without destroying it." These forbidden things are not permissible merely for study, and there is no educational purpose in drawing it. Drawing it, in itself, does not render the drawer an apostate. The questioner is advised to fear Allah and to stop the extreme obsessive thoughts regarding apostasy and leaving Islam.