I am not sure, I had a dog that gave birth to ten puppies, we were up all night helping her, but I don't remember her losing the plug, if she did I didn't see it. It could be possible she ate it. We knew though when she was ready, she showed all the classic signs. The heavy panting, she was often in her birthing box and not wanting to leave it.
She may do but it unlikely you will see it as she will probably lick it up.
Yes. My dog is pregnant and she lost hers. I wasn't sure if it was but vet confirmed it. They do lose their plug.