The physical things you're seeing are normal, too, cassingermany. The dog's body can't tell if it's pregnant or not so it just runs through the hormonal cycle as if it were. I think that's why false pregnancies are so common in unbred intact females. But all that should subside in a couple of months.
One of our rescue girls went into heat right after we got her. They did the spay anyway, and she
still had a false pregnancy. Some two months later, all of a sudden she was nesting and acting strangely and it suddenly dawned on us that if she'd been bred during her heat, she would have been whelping about then. Hormones are persistent things.
So don't be surprised if your Lily goes through the same thing.