We use either round or square - best quality and price wins. The farmer who leases our extra land has some great quality squares and he offered us a deal too good not to jump at. The previous year he only had cattle quality, so we used round. We take off 3-5 flakes and strap them together and use our bale spike to load into the round bale feeder. For the smaller amounts I just break a flake(s) apart and move it to the field with my lawn tractor cart. I love the squares.
They flake just like a small sq bale, just much larger. They are actually very easy to feed. The flakes are about 4 inches in thickness and weight about 20 pounds (type of hay dependent). They can be bent in half or ripped in half for half flakes. I put the flakes in a wheel barrow or use the tractor or a trailer/ATV set-up.
Alfalfa worked great. I once got rye in that form and it was a disaster though. The flakes didn't hold and it got everywhere.
We do not free feed any hay.
We generally don't move them once they are in our barn.