Can anyone identify this Chinese fruit and how to cook it?

No, I think they are ginkgo nuts, http://www.foodsubs.com/Nuts.html - see ginkgo nut. Sometimes it is used for dessert soup, and sometimes savory food.

If this is a jujube, it will have a crisp skin with a soft foam-like interior. The flavor is mildly sweet, like apple. If you have the variety that is used for drying, it can be very bland and almost mealy. Young jujube are greenish and turn brown as they ripen. I eat the fresh ripe jujube like an apple or pear. There's a small pit. No peeling required. Apparently you can also make a tea, syrup or candy the jujube.

Are they peeled? Hard texture? Maybe JuJubes? They look like almonds to me, but I know they aren't. If you 'search' on the Internet type in Chinese fruit and all kinds of photos come up. You should be able to identify them by all the photos. Good Luck! BB