1. Can a warrior be placed in a way that its guarded area overlaps another player's warrior's guarded area? If yes, does that mean no one can place settlements on the overlapping hexes until a warrior is moved or both of these players can?
2. The rules state that a Wagon and a Lighthouse is regarded as a settlement for building purposes but it doesn't say anything like this about the Warrior. So am I right to think the warrior shouldn't be considered for adjacency purposes?
The guarded areas can overlap; that just means there are two things preventing pieces from going there.
The warrior prevents pieces from going adjacent to it. So, whether it "counts for adjacency" or not doesn't mean much. I can answer anyway though. It would count except it prevents pieces from going adjacent to it.