I did a couple of 'Sherwood' missions, leaving most of the band behind, but nothing gets produced? I used individual characters to 'pick up' the scroll specific to a given crafting/gathering item, but nothing showed up in their inventory, anywhere on the map and nothing is mentioned in the 'summary scroll'. Specific icons were present over the characters which left at the camp, I tried also 'entering the hut' with the characters, but to no avail. What's more, while characters I left training are mentioned in the 'summary scroll', their stats are unchanged. Am I doing something wrong, is there some kind of bug or what?

Hardly ever, if at all, those things get crafted while you're doing generic Sherwood-based missions.
If, however, you leave people with theirs given chores while doing an actual storyline mission, you'll always end up with at least some new resources stockpiled.