How far do I need to be from the Iron Golem farm for it to work?

Solution 1:

From the Minecraft wiki:

Chunks near the player are loaded into memory. The range depends on the Render Distance setting. These chunks may have activity (mobs spawning, trees growing, water flowing, dropped items disappearing etc.), while chunks outside of the range are inactive, and are stored on the disk. Chunks will not save again if they were saved in the last 30 seconds.

Chunks that aren't loaded don't change at all until they're loaded. So if you're 230 blocks away from your iron farm, the render distance would have to be at least 15 chunks (230 % 16 rounded up) for the iron farm to work.