The hospital was on D deck on the starboard side, in line with the fourth funnel. There was also a small hospital for the crew on C deck, behind the foremast. Unfortunately there are no photos. The Post Office was on the starboard side of G deck near the bow, with the Mail Room directly below. Again there are no photographs of this area. There was no public access to the Post Office, but stamps, paper and envelopes could be obtained from the Pursers and letters could be given to a Purser or posted in boxes like one outside the 2nd Class library.
Though it was mentioned in some newspaper accounts before the ship was built, there was no photographic darkroom on the Titanic.
The darkroom appeared only on some early plans for Olympic, in the location you mention (aft of the lounge, starboard side). Some people have made the mistake of thinking that Titanic was the same, but it was different in many ways. On Titanic that location was a cloakroom, as shown on the deck plans which were given to 1st Class passengers. There was no darkroom anywhere on the ship.
I can't make it work. It may have been the picture on page 79 of Titanic Voices. That used to be on another site, but it's gone now. Whether it's really the mail room on Titanic is another thing. Perhaps careful checks against photos of the mail clerks would show if it's for real