As I often say when these friendly game questions come up, please remember you're not a casino nor a cardroom, you're playing with friends so keep it friendly! So just keep this in mind when deciding what to do to keep the game fun for everyone, mistakes happen. I'll say you can't really have a misdeal after action has happened. This can vary by casino, tournament rule sets or cardroom rules, but generally once every player has received their first card, misdeals aren't call. I've never seen a misdeal be called after money has been put into a pot, ever, you just have to deal with as best as you can.
Q1 - Normally I'd close this but given your second question is not answered I'll leave it open. Your first question is answered here - What happens if the card wasn't burned?
Q2 - You do your best in this situation as it can depend. It happens at some point to any dealer. So if the card has landed on the table after the burn it's a bit late, often I've seen floor just rule that the player who hasn't acted yet gets their action limited to check or call only where the mix up has happened. You can argue that it's not fair to that player, but it's the fairest thing for the integrity of the game at that point as now that person can bet having extra knowledge. Same for other players with a draw, they can either call knowing they hit, or fold knowing they missed. It's just the fairest to limit the action from what I've seen most floors do. The player will have normal actions after that mistake has been dealt with, i.e. if the turn was shown to early, the player can check or call on the flop, then on the turn actions are restored to normal. A caveat for this I've seen was where the turn came out as the player who hadn't finished action said raise, they were bound to a min-raise in the case.
In cases where the dealer is stopped before showing the card, just protect the card until the player has acted.
One thing I'll add to both questions is some decisions I've seen some floors do a few times (granted many years ago now). Example I often saw was flop was fine, but a mistake was made on the turn, either missing burn card or just showed the card too early. So what the floor did was told the dealer, burn for the river (in cases where the turn was placed without a burn, the floor asked the dealer to burn twice to get to the 'true' river), and place the river face down. This helped preserve the 'true' river. Following this the dealer was asked to reshuffle the deck (just the deck, do not include the burnt cards), burn and play that card as the turn.
I think what ever decision you decide to make, make it as a group to what seems the most fair for everyone. It's a friendly home-game, always remember that and always keep it that way when possible.