About Mr. Randolph's son
The chief reason why Mr. Randolph took Sara's father under his care is because he is in the same regiment as his son and might have knowledge of his whereabouts or fate.
In the end, what we find out is that Captain Crewe had tried to help Mr. Randolph's son, according to Mr. Randolph's line "No more than you(Captain Crewe) tried to do for my son". But that still leaves one question: Is Mr. Randolph's son alive or not?