First of all, I suggest you get a copy of Robert's Rules of Poker. The current version is "11" and can easily be found using Google. Now to your specific questions:
1. Exposed Card - Per RRoP, Chap. Two, "Professional Poker Rules", Section 5, "Hold'em", sub. 1, (Note: This is the section for Casinos and is followed by every casino I have ever played in. Chet) "If the initial holecard dealt to the first or second player is exposed, a misdeal results. The dealer will retrieve the card, reshuffle, and recut the cards. If any other holdcard is exposed due to a dealer error, the deal continues. The exposed card may not be kept. After completing the hand, the dealer replaces the card with the top card on the deck, and the exposed card is then used for the burncard. (emphasis added) If more than one holecard is exposed, this is a misdeal and there must be a redeal."
In the section on Private Games, the rule is essentially the same, except a misdeal results ONLY if the first holecard dealt is exposed. The rest of the rule is identical.
2. Boxed Card - Again per RRoP, Chap. Two, Section 3.4, "Irregularities", sub 7, "A card discovered face-up in the deck (boxed card) will be treated as a meaningless scrap of paper. A card begin treated as a scrap of paper will be replaced by the next card below it in the deck, except when the next card has already been dealt face-down to another player and mixed in with other downcards. In that case, the card that was face-up in the deck will be replaced after all other cards are dealt for that round.
In the section on Private Games, the rule is identical.
All this said, it is entirely possible that a local cardroom/casino has established house rules which differ. So it is always a good idea when visiting a cardroom/casino for the first time to inquire about their house rules.
Hope this helps!