Why these sentences are wrong? 1. They are afraid people 2. The cost factor is cruel. 3. The village post office is local.?

1. They are afraid people.
"afraid" is an adjective (predicative, modifying the subject "They") and cannot take "people" as object.
To correct, put a preposition after "afraid" to take on the object.
~ They are afraid of people.

2. The cost factor is cruel.
"cruel", when used as predicative adjective (after noun), has to be personal. For impersonal use, it has to be attributive (before noun)
~ It is a cruel cost factor.

3. The village post office is local.?
"local" is nornally used as attributive adjective (before noun).
~ It is the local village post office.