Let's suppose that on day 5 of the first week the general event turns out to be "Jimmy says he's got some real juicy info for you". So he's placed at Old War Memorial.

Then, at the start of day 1 of the second week (according to the official FAQ), he's moved again because of the case-specific event.

Does this "ends" the general event regarding Jimmy?

The rules are not clear about this. In the "Resolving general events" paragraph they say: "An event's effect can end in three different ways: the NPC associated with it can be eliminated or redirected to a new event;..."

Does the specific event meddling of the NPCs counts as "redirecting to a new event"?