1, Check your local glass or plastic supply stores, for food grade plastic. Our local glass store does a lot of work in the food industry and they do a lot of cutting tables and the like. They can cut a chunk that will span the sink if you so desire. The material comes in 3/8 or 1/4" thickness.
2, Mat, they lay flatter and don't flip up with every breeze.
3, Ditto, ditto and ditto.
When I was a kid I was going nowhere fast, now I'm an old man I'm going everywhere slow.