After installing the game, patch 3.1, copying the saves, the mod with templates, and the map, my respected opponent from round 7 (Alex_NV) and I were unable to load the saved game for 40 minutes. If Alex_NV tries to load it, the message is: checksum mismatch, etc. If I try to load the game, the message is: the saved game is corrupted or the map does not exist...

The game was saved on week 6, and it seems it was about to be the final round. At that point, I had completed my main objective, and my opponent had completed about 40% of their main objective (also by me). The stats of my opponent's main hero and my main hero are approximately equal...

No, that's not the case. In 3.1, you no longer need to include the map if it wasn't created using the new generator, as is the case here.
Checksum mismatch... it's possible that you have files with different dates in the mods folder (or someone forgot to change something). Check the identity of the files in the folder.
There's no name in the save... Well, it's unlikely, but could someone have confused the names? It's more likely that the last autosave was made when someone had already exited the game. Try the second-to-last save. If it also doesn't load with the name mention... let someone send it to another player.