Cooked food waste is bad news in a compost heap, as is anything at all of animal origin except for herbivore droppings (horse, rabbit, chicken, sheep=good, dog, cat, human=bad). Hair, maybe. I'm suspicious of eggshells for the same reason. I have no desire to attract rats. Wood or charcoal residue from my firepit gets sprinkled on in small amounts as it's a useful source of potash. I don't use newspaper as I don't want the chemicals from newsprint. I've come to regard compost starters/accelerators as a waste of money as I get lovely compost without them anyway. I've never bothered to enclose or cover my compost heaps though they are quite sheltered. A good turning-over once or twice does the trick. The only vertebrate beasts that show any interest in my heaps are grass snakes and slow worms, both of which breed therein every year, which is fine by me. I doubt whether the frogs and toads would agree. I haven't got potato eelworm or brassica clubroot in my garden, so I won't compost shop-bought potato peelings or brassica trimmings. I have got white rot, which has black spores that can live in soil for 20 years, so growing onions, shallots, leeks or garlic is a waste of time, and a smelly one at that. Nothing smells worse than rotting onions unless you know different...