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I would wait until Sept/Oct to move the seedlings. You could move it now but you will have to coddle it during hot weather. That means more frequent watering and providing shade from afternoon sun. Even after leaf fall, the roots keep working until the ground freezes. Make sure the soil drains well and mulch to reduce the amount of soil freeze and thaw. Don't prune or fertilize yet but do make sure it is well-watered going into winter. Obviously, you want to bring as much of the root-ball as you can manage. Gently scrape the soil and see where the roots are. Maples are fairly shallow rooted - no deep digging to worry about. For older trees the rule is to start digging out one foot for every inch of trunk diameter. The Japanese maple is a highly bred tree; usually these do not come true from seed. Seed-grown stock will not look like the parent plant if it was a cultivar and not Acer palmatum "Atropurpurpeum".

Most Japanese maples can only go down to zone 5. Some are hardy to 4. This being the case, I would advise to be on the safe side, and bring the trees in on the coldest nights of winter. At least til they are a few years old.

Here is some more information on the care of the tree: https://www.google.com/search?q=japanese+maple+hardiness&oq=japanese+maple+hardiness&aqs=chrome.0.0l4.5915j0j7&client=ubuntu&sourceid=chrome&ie=UTF-8

This article should help you
https://www.gardeningknowhow.com/ornamental/trees/japanese-maple/japanese-maple-care-pruning.htm

Yes, you can grow daisies and other plants under a Japanese maple. Here is some advice on planting under trees:
https://www.gardeningknowhow.com/ornamental/trees/tgen/planting-garden-beneath-trees.htm
https://www.gardeningknowhow.com/ornamental/groundcover/gcgen/ground-covers-under-trees.htm

The pictures were uploaded upside down for some reason. I don't understand that.