You can use it as a mulch around most things, patticularly beans of all kinds, peas, potatoes etc. It probably won`t contain as many weed seeds as your own soil does, and used thickly will suppress the weeds in the soil. It will also prevent the soil surface getting `beaten up` in heavy rain. The drawbacks are that slugs sometimes take refuge under it, and in windy weather some of it will end up in your neighbours` plots.
As for grass cuttings, the answer is `yes`. A 2 - 3 in. layer, but not if you have used any form of lawn weedkiller lately, and check your lawn for any seeding grass or weeds first.
