Do the trapped souls in the Reaper/Shinigami suffer?
In the manga chapter 124, Sarutobi tells Orochimaru what happens to the souls who are sealed by the Shiki Fujin.

With this jutsu, the one whose soul is sealed will suffer for all eternity in the belly of death, never gaining release. The one who is sealed and the one who performed the seal, their souls will mingle, hating each other and battling the other for all eternity.


This would happen in the normal case, which is when a shinobi uses the Shiki Fujin to seal his enemy's soul along with his own. Naturally, their souls would continue to fight after being sealed inside the Shinigami's stomach.
However, Sarutobi used it to seal his former teachers, Hashirama and Tobirama, who were only fighting him because they were under Orochimaru's Edo Tensei control. After being sealed, there was no reason for them to continue fighting, and hence, when they were released, they don't look like they were suffering or exhausted from battle.
The Fourth Hokage was sealed with the Yin-Kyuubi, and he presumably ended his battle long ago, as described here, so he had no reason to be suffering either.