I'm making a guess here BUT the plant with the lace cut leaf looks very like the herbaceous Geranium and the close up picture of the strappy leaves look like one of the onion family BUT when I looked at the pic that was further back from camera lenz, the strappy leaves looked like grass.
Maybe someone else can give other ideas.
To separate the plants, use your garden fork, (about 6-8 inches out from the plant STEMS so lift the foliage up to find the stems exiting the soil) sink fork way down, you may have to actually stand on fork to get depth, anyway, do this all the way around the plant and then as you place the fork in again, use a lifting movement, this should allow the plants to begin to rise, keep gently going round the clump unto the plant and roots are free.
Lift the plant in hand, shake dirt away, then look at roots to see where the plants can gently be tugged apart, you might have to use a bit of power in your hands to tug BUT make sure you don't break the foliage away from the roots.
Once parted, check there are no bits of roots from different plants left.
Dig a hole and replant, make sure you water well especially in warm / hot weather, IF you can I would add compost or other type of humus to planting area to help enrich the soil at planting and it helps add air, nutrients and retain a little moisture around the roots.
Long drawn out but hope it helps you out.