Sure its useful in conditioning soil, but you seem a bit worked up and stressed about it to be honest. Gardening shouldn't be such a stressful hobby. First thing is turn that compost. It will take forever otherwise. Keep the greens/browns balanced in that too, and dont let it dry out. You sure can use your grass cuttings to mulch, lay a few layers of newpaper out, then cover with your cuttings, then water. After a few days dig that in, it will really help. It rots down pretty quick too. Any organic matter you have will help to mulch.