Some portions of the block are from the kite shape, and although I thought at first there was some curved piecing, that may just be an optical illusion ?

when I look at it, I see a 4 point star with an x

Oh....and BTW persistent, welcome to the forum! Would enjoy hearing about your quilting journey!

I have in idea, very interesting!

If you would look at the secondary picture, it looks round, like a "fox & goose track" as in the children's game in the snow. I do not know how old that is either. Good luck in finding the real name but I would say to go to Barbara Brackman's site and find or rule out a civil war pattern. I would search & search too if it were mine.

The lighter fabric looks silk like. Such a pretty quilt. It reminds me of a stained glass window.

The 2nd pic shows the swastikas they are very hard to see. The picture was taken at the right angle to see them. Unless the light right you don't even notice they are there thread color is same as background but the thread is shiny so the light makes them pop out. if you look at the full pic you don't see them no matter how close you zoom. Nobody in the family even knew the hidden swasikas was there .

Could you post a closeup of some of the other darker blue fabrics? The one you already posted is dotted, and those aren't the easiest patterns to date because they have been used forever and ever (same thing goes for checks, plaids, stripes). I haven't researched that pattern, but could probably give you a respectable age estimate from the patterns in the darker blues there.

This is what I've found via the internet; There is the right facing swastika, or the one highjacked by the Nazi party, which represents the evolution of the universe (pravritti), and the left-facing swastika, which symbolizes the involution of the universe (Nivritti, the process that allows creation to happen).

About the "swastika" pattern in the fabric. This symbol is older then dirt and goes much farther back in history than WWII, and may not be what we see at first glance, and if it is then it is a piece of history, not to be shocked by it, but learned about and history passed on so as not to forget.

As for the quilt, It is an interesting pattern I have never seen before. I think you may want to look into it further by a conservator.
peace