That is a slime mold. Pretty harmless and will go away with drier weather.

Most likely is Lirope - muscari is the clumper, watch out for spicata , which is a running, spreader - best planted in a contained area. Yes, cut it to the ground in late winter/early spring.

gramma jan, my first question would be about the amount of sun they would get? Most of the grasses bloom best in sun locations. Deschampsia (tufted hair grass) will tolerate some shade but it has very delicate, airy looking blooms. It sounds like you are looking for something more like a miscanthus bloom. At any rate I've included a link to a publication from the U of MN on hardy ornamental grasses. Here is a link that might be useful: Ornamental grasses

Liriope comes in two types - clumping and spreading. Liriope spicata is the spreading type and Liriope muscari is the clumping type. Note - clumping grasses or grass-like plants DO increase in size with time.....they just do not expand with vigor or uncontrollably like the spreading or running types do. In addition to the hakone grass, I'd consider some of the Japanese sedges - Carex morrowii or Carex oshimensis. Most are well-behaved clumpers, although Carex morrowii 'Ice Dance' does expand rather vigorously for this species.