I would prefer not to mention the cards as I am hoping to use this at cities, but what is the minimum amount of basics I am allowed to run? and with that being said, what is the mulligan limit?
In order for a deck to be legal, it must consist of at least 1 Basic Pokemon.
As for mulligans, there is no limit. However, they are an option for your opponent; they are not required to draw a card. Also, I believe, after a while, the TO will instruct you to flip over cards from your deck until you reveal a basic Pokemon, and/or search and switch your prize cards.
Anyway, during the HP-MT era, it did happen quite a lot that there were 10+ mulligans due to decks running only 4 basics (4 Chansey), then indeed the judge could come over to do afformentioned card-flipping.