If there were no gravity and the normal force was an active force (someone pushing block c), then some of that force would be transferred through block c to the next block. But, the normal force is simply opposing gravity, so there is no net force on block c.
Of course, some of the force is transferred as the normal force between blocks c and b.
And, there is nothing special about the blocks, the same sort of internal forces are acting within each block. The bottom of each block is supporting all the block and the ones above it, whereas the top of each block is supporting only the blocks above it.