Minecraft – Within how many blocks do I have to be for wheat to grow

This is essentially how Minecraft operates: when items spawn inside your crushing block, the game tries to move them somewhere valid. Any non-solid block, like slabs or stairs, that won't push items, also won't crush chickens. Double thick walls may help, but not guaranteed. The game will just try to push items harder.

The solution is to put some kind of non-full-height block above the hoppers. This way, chickens will still have their heads suffocated by a block above, but their legs and dropped items will be in a valid space above a lower block's surface. Hoppers suck items in from the whole block space above them, so that would not be a problem.

Testing indicates that the obvious choice of short block - the Slab - works perfectly.

Also check the list of block heights here: http://minecraft.gamepedia.com/Solid_block#Heights

As @09stephenb stated correctly, on Single Player Minecraft, only chunks in render distance are updated. This begs the question: what is the render distance for Single Player? You can adjust it in the Options > Video Options page, at the Render Distance option.

_{(source: cursecdn.com)}

The higher the number of chunks, the farther you can see. Hence, more blocks are rendered, which might lower the game's performance. For the picture's example of 12 chunks (which is the default), you can see blocks in a 192 block radius (give or take).

Note however that chunks are 16 blocks wide, 16 blocks long, and 256 blocks deep. If you are mining very far below your farm, it will continue to be calculated. What matters most is horizontal distance.