Squill is
Scilla, you may know it under that name. It is nice all thru a lawn except that, like having crocus or grape hyacinths all thru your lawn, it does not mix well with either a) dense fast-growing turf or b) a frequent low lawnmowing regime. Works best IME when done in kind-of-scraggly-and-struggling turf in open shade under trees, and located where you don't mind the lawn looking kind of rough til the leaves are gone.
[quote[Well, if you remember - help me remember these strange grass-like things in my lawn, please.[/quote
PICS, we need PICS

(and could probably also identify them...) (e.t.a. -are they purple flowered? Could they be very stunted Camassia, or could they be native blue-eyed grass Sisyrinchium somethingorother?)
Daffodils: I would not divide daffodils now while they are green, unless there was no other choice than to take a flier on it.
But you can get okay results IME by dividing or moving them once the foliage has almost completely died down in several months. That is, when you've left it as long as you possibly can and still FIND the things

Be gentle, and although they may not bloom well the next year I've had good luck establishing them longterm that way.
Good luck, have fun,
Pat