If I remember correctly, clues held by investigators are kept.
Not quite. In the first couple of scenarios (2 through 6, I think) you start without any clue markers. However, you get to put those left over from the previous scenario at some location and can get them instead of having an encounter. The later scenarios work as normal.
And no, you never get to keep your items - that would make the game way too easy.
Well, in the 2nd spanish league, there are 3 specific rule. The second one starts with, i'm quoting: "Common Items, Unique Items, Spells, Skills, Madness and Injury cards are kept from scenario to scenario as long as the player maintains the same investigator"
I think you're referring to another league.