The correct answers are I have lived in this haunted castle for three centuries., I lived in a damp cave before I moved here., and The local villagers haven't visited me since last Halloween.

The Present Perfect is used for situations that started in the past and continue today. Use for with durations (three centuries) and since with specific starting points (last Halloween).

The Past Simple is used for finished situations or specific past events (like moving in 1890).

"since three centuries" is incorrect because "three centuries" is a duration, not a starting point. "have moved... in 1890" is incorrect because 1890 is a specific, finished time in the past.