Here's what I know about the # cards.
As to the sets with the # on the card, there was a seller on ebay a number of years ago, not sure if they are still selling there or not, that had these cards for sale, and it seemed like they had a good quantity of them in mint condition. The seller listing said these cards were originally used in a promotion at movie theaters, I think in the United States, and they included a black and white photograph of a theater display with these cards on display at an old movie theater. (I thought I might have saved a scan of the photo, but I can't find it on my computer, maybe someone else saved a scan of the photo.)
The seller was selling the cards in small groups of about 20 cards at a time I think, and I bought one of the lots. In the lot, there were both types of cards with the # on the front, the kind with the dash and the kind without. Below are two cards I got in my group:
Both types that I got had blank backs. The seller sold many more lots of these, they had a good quantity. I don't know why PSA identifies them as Val Gum, I don't think they are Val Gum, even the ones that say Val Gum on the back. I agree with all the points that Mark makes about them.
I'm still not sure if these cards were ever given out at theaters or if someone just made them to sell to the collector market at some point. Since I regularly searched for old movie cards and never saw these from any other sellers, I kind of leaned toward them not being legit old cards for a while, but then I did see a card that looked legit from the 1950s in this design for sale on ebay with an ad on the back:
So now I don't really know either way, they could be legit movie theater promotion cards that were unsold at the time and found their way to an ebay seller later.