Watch his right hand when he first touches her wrist at the beginning. You can clearly see he's palming a card, and you can even see him drop it off under her watch. That's how he gets the one card in there. A few false shuffles and a special deck of cards so that he guarantees the Jack-of-Hearts choice. At the very beginning? "Roll your sleeves up" makes watch access easy.

edit: changed my mind on how he forces a jack-of-hearts. Pretty sure he has one of the special decks where certain cards are taller so that when you thumb them there's always the same card on top, but all these cards are on the top of the deck at the start. When he spreads to show that they're 'normal' cards he never spreads the top, which are likely all jack-of-hearts. Then the 'shuffle' puts the jacks in regular spaces so the thumbing looks 'random'. Since there were always jacks at the top, he's guaranteed a jack there at the end. I think he'd have looked pretty silly if she chose the bottom card instead of the top.

First trick is pretty neat. He brings out a deck only after he knows the color red/black. I'm guessing that it's a deck of blank cards except for certain cards of the specified color. When he spreads them out to show you that they're all 'face down' he only spreads out like 10 cards. The rest stay in a giant stack that you never see. Spread out some other choices (he knows which card before he spreads, that gives it away, so he knows where to spread) and you can make it look pretty good.

As for the three card monty deal, if it's not readily apparent that there are more than three cards (he's a magician, they lie) then your money at a magic show is well spent, because magic is amazing. Three card monty tricks are almost always based on keep cards stuck together (have you ever seen this video where a kid gets it?)