The character of Colonel Laurence St Clare is based on Lieutenant-Colonel Jack Churchill, a British officer who carried a Scottish broadsword into battle. He is quoted as saying "any officer who goes into action without his sword is improperly dressed". He also carried a longbow and arrows, and a set of bagpipes into battle.
"Dolce Et Decorum Est Pro Patria Mori" is Latin and means "it is sweet and honourable to die for the fatherland."
Father Brown gives the last rites to the murder victim as he does in many episodes. Priests will often do this even if the person appears obviously, but recently deceased on the chance that there is still a flicker of life.
In this episode, as in many others, Father Brown appears to administer the "Last Rites" to an already dead person. The Last Rites are literally the last intervention by a priest in a person's life (once you're dead it's too late)