Is it permissible for me to be absent from congregational prayers at the mosque and pray at home if going to the mosque causes me headaches and distress, taking into account the long distance and the unavailability of transportation, and considering the saying of the Messenger of Allah (peace be upon him): "There should be no harm or reciprocal harm" and "Religion is ease"?

What you mentioned about a headache does not permit you to miss the congregational Dhuhr prayer in the mosque and pray in your home, because missing congregational prayer is only permissible for a valid excuse. If the illness is minor and does not make it difficult to attend, such as a toothache, a slight headache, or a mild fever, then this is not an excuse. If you hear the call (to prayer) with the usual sound, then you are commanded to join the congregation. However, if you are far away and cannot hear the call to prayer without a loudspeaker, then you may pray in your home or with some of your neighbors.