1. If the heroes won the encounter, but did not search the search spots, do they allowed to do so after meeting the victory conditions? Same question for the situation when OL wins the encounter.

2. Syndrael ability: "If you have not moved during this turn, you recover 2 fatigue at the end of your turn". "Have not moved" refers to ANY movement, i.e. if this hero moved by fatigue, it counts as movement for this ability?

RussianDM said:

No, in either case. The heroes have to search the markers to claim the benefits. You could run this as a house rule, if your group is one of those who feels like 2E favors the overlord - this effectively gives the heroes a free 25 gold per hero in every encounter (double for most quests).

RussianDM said:

I read this as ANY movement - the hero has to end the turn having not left the square they started in.

Thanks for supporting my thoughts

Usually, the quest ends immediately after one side claims victory. Sacrificing some of your actions to search is part of the general strategy. However, sometimes when you've locked down a quest, you can prolong it for a few turns to make some search actions before completing the victory. eg Cardinal's Plight pt 2. Only zombies can attack the Cardinal, so once you've opened the door and killed off the zombies, you can send a few runners to search while killing any zombies that respawn. Then move the Cardinal off the map after you have finished searching.

Missing search spots will maybe hit my players, but I think it is more than logical - not to give something that they did not fought for.

Correct. A lot of players are in the RPG mind set. "Kill the monsters, loot the room!" But, that's not the way it works. It's more like a video game. If you go through a level of a video game and exit the map, you don't get all the goodies you overlooked.