Some cards refer to the number of stars a character has. Does a character in bot mode have any stars?
[Source: WotC] 
Yes. Even though the stars are printed on the alt mode side of the card, the character has that number of stars no matter which mode it’s in.
Please explain the general rules on the battle cards with stars on the bottom? If you already have a 25-character deck, can you still put them in your deck for pip purposes and/or play them? Why is there a star on the bottom? Or do you have to have extra stars available to even put it into your battle deck?
[Source: WotC]
You have to have extra stars available to put star battle cards in your battle deck.
