I have tried to clarify my definition of the two philosophies and spell out their implications.
Squarism: Imagine a square grid laid out across the playing area that lines up exactly with the normal tiles. A tile is one of these squares, so long as it is occupied by at least one halfling, German castle, normal tile, abbey etc.
Cardboardism: A tile is a piece of cardboard that has been laid in a legal position on the Carcassonne board.
Q1: What are the rules for a monastery (or German castle) to be complete?
S1: Each of the surrounding 8 (10) tiles must be laid.
C1: Each of the surrounding 8 (10) tile spaces must be occupied by at least 1 tile.
A1: This implies no difference in actual game play. Similarly there is no difference in the rules for the placing of abbeys.
Q2: How is a monastery (or German castle) to be scored?
S2: The feature scores for every tile it occupies. It follows that under squarism a completed moanstery (German castle) always scores exactly 9 (12).
C2: The feature scores for every tile it occupies. It follows that under cardboardism a completed moanstery (German castle) scores between 7 (12) and 17 (19) inclusive.
Q3: What are the rules for a road to be complete?
A3: I'm not sure but I believe that there must be no gaps from end to end and that this does not depend on philosophy.
Q4: What are the rules for a city to be complete?
A3: I'm not sure but I believe that, unless the la Porxada condition is met, there must be no gaps either on the edge or in the interior and that this does not depend on philosophy.
Q5: How are cities roads to be scored?
A5: The feature scores the appropriate amount for every tile it occupies (German cathedrals and city shields can score more). It follows that halflings cause roads and cities to score more under cardboardism.
Q6: Could an unmatched halfling prevent two fields from being joined.
A6: I think so but I think this is a separate question to cardboardism versus squarism.
Q7: How far can a flier fly?
A7: 1, 2 or 3 tiles. Halflings under cardboardism can reduce the options. German castles under cardboardism increases the options, since the castle itself and the length of the tile are available even if they are off angle.
Q8: Goldmines?
S8: Given two matching halflings a gold ingot is available to features on the other. An ingot must be placed on one half of the castle. The castle itself cannot benefit from the gold.
C8: Given two matching halflings a gold ingot is NOT automatically available to features on the other. An ingot on a German castle is available to all features including the castle itself.
Q8: Little buildings?
S8: Given two matching halflings a little building is available to features on the other. An little building must be placed on one half of the castle. The castle itself cannot benefit from the little building.
C8: Given two matching halflings a little building is NOT automatically available to features on the other. An little building on a German castle is available to all features including the castle itself.
Q9: The plague? Towers? The dragon?
S9: Under squarism movement is natural and intuitive. A single unmatched halfling does not block movement or capture.
C9: The whole notion of the direction breaks down and has to be defined in several ad hoc rules.