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A manual auger is a great idea for loosening it up and turning the compost inside. I'm not sure about composting in temperatures like that. It never gets that hot here sadly.
Not necessary at all, it just came with the bin. It just helped avoid digging out gravel when digging out compost. A layer of sticks will eventually rot away so I wouldnt bother. Just try not to dig out the gravel.
Yet Another Daft Punk Coffee Table (5x5 LED Matrix)