Neem oil will not harm the compost. It will keep sewer flies and such out.
You can compost your waste. The ratio depends on what all you are adding. Generally referred to as dry/wet or brown/green ratio in compost. Fall leaves, woody stems, egg shells, coffee grounds would be dry, brown. The high fiber carbon materials. Things like grass clippings, green leaves, garden food scraps would be wet, green. The high nitrogen materials. You want 2 parts carbon to one part nitrogen in your compost mix. If your carbon is too high there won't be enough microbes to break it down. Nitrogen too high you will explode the microbe growth and get a stinky soup. If you need more carbon a bag of wood chips can be used.