Soft Matzoh on Pesach?

Is soft matzoh kosher lepesach 'al pi Minhog Ashkenaz?

My understanding was that Ashkenazim were allowed to eat it as it is not chometz, but should not use it as the mitzvah matzoh at the seder.

Thanks, a good article.
Rambam says to take two Matsot for Pesah, divide one in half, to put a half inside a whole folded-one. I think, it is possible only with the soft Matsah. Maybe he read about it in Yerushalmi (not Babli)?

Haggadah describes the custom of Babli-hahamim to study and discuss Pesah-laws during to all Pesah-night. It means they didn't sleep. Is that the Mosaic-custom or just Mishnaic?

Here in the US, R' Schachter of YU has matired it for Ashkenazim, but R' Elyashiv ז”ל was of the opinion that it's ossur, so it's a fairly fraught machlaukes, particularly among those who don't disregard YU out of hand.