When an Encounter provides multiple types of Tokens (e.g., Grave Robbers, The Colonel, etc.), how do you determine what type of Encounter it is for purposes of cards such as Hook 'n Rope (you don't get a terrible thing token when failing Pitfall Encounters) or for purposes of achievements? Is it all of those types? Just the first type?
It's all of those types if more than one type is listed.
Also, am I misreading The Baroness and The Occultist somehow? (Run of 4 dice starting at 3 or higher...how could it be higher? Occultist is a run of 3 dice starting at 4 or higher.) Maybe this was just a misprint.
You are reading it correct.
If a run is mentioned they just always used this convention/wording even if the run can't be higher.