What are the scoring criteria in Carcassonne for farmers regarding grassland connectivity and field boundary division?

When playing the base version of Carcassonne, there is often unclear discussion about scoring for grasslands (farmers): When multiple grassland tiles are connected into a large field as tiles are placed, if there are two completely closed castles adjacent to this grassland, and the outer perimeter of the castles is separated by roads, which castles can the farmer actually score for? Does a road necessarily cut off the connectivity of the grassland?

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