NO! Do NOT use loose paver sand near your chickens unless you're using it to fill cracks between concrete patio stones, hosing it down and allowing it to solidify first. Paver sand has chemicals that react with moisture to harden just like concrete. If a bird eats enough of the sand, it could potentially block its digestive system and kill the bird. You wouldn't feed your chickens powdered cement would you? This would be no different.
Yes-Washed concrete sand works great. I have it in my run and I love it...Easy to scoop the poop and dries very quickly after a rain. Also doesn't get too hot when it's 95 degrees outside... Girls takes dust baths in it, too..
It doesn't get hard when it gets wet. Concrete sand is just a less washed and has less 'fine' material. It is used in concrete but also as fill material. The reason it is because it is less expensive and also because it doesn't clump together allowing for better drainage. Concrete sand is simply the sand that is taken out of a sand pit and is not over processed. The size of the aggregate and the overall composition of the product will change from quarry to quarry but it is a good product to use. Spending more for sand that has a smaller aggregate or a more washed material is not giving a better product for the purpose you are using it for.
There is a product that comes in a bucket that is designed to work exactly like you mention and you would be correct for this product. However I beleive the OP is asking about very coarse regular sand that is used for making concrete. The product you mention is extremely fine and would be quite expensive for making concrete.