The other old man is the Ronin and General's mentor.
"Other old man" meaning the old man sitting in a chair in the photograph who isn't the boss called Old Man. In the pre-mission blurb when she goes to assassinate the General, the Ronin mentions that he and she were taught by the same mentor. The old man's clothing resembles a traditional Samurai, and his absence in the game could be due to the Mentor Occupational Hazard.
No idea who the sickly-looking man is.
- Isn't it obvious? It's Mr. Poe from A Series of Unfortunate Events! Guy has terrible luck with orphans...