"O God, through whose mercy the souls of the faithful are at rest"
The author treats the chaplain as if he said, "through whose mercy the soul of this faithful one is at rest." He did not, of course.
"Bless this grave... To bless means to make happy; "
Uh, no. One who is blessed is made happy, but they are not synonyms. That's how silly translations like "Wei Li's Happy Chicken Buffet" happen.
Bless:
To make holy by religious rite; sanctify.
To make the sign of the cross over so as to sanctify.
To invoke divine favor upon.
To honor as holy; glorify: Bless the Lord.
To confer well-being or prosperity on.
To endow, as with talent.
Blessing a grave would make the gravesite a source of comfort for those who mourn there.
"We must assume that he is appealing to the heretical high-church Anglican theory of baptismal regeneration"
I don't know how you want to twist scripture to call baptismal regeneration a heresy, if you call going near the subject appealing to it, the cleric appealed to it far less than Jesus did.
"Asked whether all soldiers were cleansed by water and therefore going to heaven,"
God ordains all things. Praying does not change his mind. Yet we in hope pray that he has already willed things to be. Thus, it is virtuous to pray in the reasonable expectation that the person was christian, even if we cannot be 100% sure. Just like we would pray for someone we knew had been Christian, without being 100% sure he had not apostasized.
Besides, there are no atheists in foxholes, remember? :^D
"Why do you not mention or pray in the name of Jesus Christ, which is the usual practice in Christian services? "
It is troublesome the way that Jesus Christ is hidden away from public rites... this I will agree with the post with.