Compost is slightly different to FYM - farm yard manure. FYM is high in nitrogen and is used for leafy crops and if it has animal bedding in then it also supplies bulk to the soil for the lumbricus earthworms to work in. You can stack manure in a neat heap, but you need to do it on soil to take the runoff, unless it's on concrete and you have an inbuilt channel to some collection point. Compost is for all your garden material, minus seeding and infected weeds and poisonous plants, plus cage cleanings from guinea pigs, rabbits etc. This is used for a general fertiliser for your veggie patch and also bulks up the soil, contributing to soil structure. The worms will work that in too if you go for no dig.
You can mix both together to get a fertile version of garden compost.
In fact you can store both types in composting boxes, min 3 feet cubed. You don't put in things like meat, cheese, table scraps and so on, but any veggie scraps are fine.
You need to turn a heap so you need a min of 2 boxes in a row, preferably 3. Turning the heap brings uncomposted material into the middle of the heap to break down further and helps aerate the mix. By turning into an empty box, you then have an empty one to start the next heap while the first is carrying on composting. If you turn again into box no 3 then you will have really well made compost which you can use straight from the 3rd box. Otherwise it can be best to spread the less well composted stuff on the ground to break down more, or put it in the bottom of your bean trench.
yes, compost should be covered. It can be a lid, a piece of tin, a felted sheeps fleece, an old wool carpet or some old wool jumpers.
Rats aren't much of a problem and if they are, set the dog on them.
Compost is magic