Also dealers if you notice when they are done dealing will remove the burn card and place it on top of the remaining cards (or they should) and then they kill the losing hands and place them on top of the burn card, this is to insure that if a problem is found they can get the players cards back and still have the deck in its normal order.
now I had a similar situation happen to me at Mountaineer I was playing 1-2 NL and I had Aces and the board was A 3 K 9 4 the pot was at around $35 and the other player bet $40 I called and flipped my Trips he looked at his cards looked at the board and said nice hand and turned his cards face up and said I missed my straight dealer mucked all the cards awarded me the pot and placed those cards in the shuffle machine, then another player said wait you had 2 5 right and a few others said yea then you did have the straight. Now I did not see his cards but the players at the other end said he did indeed have 2 5. So they called over a floor person we told him what happened and they said that they would go back and look at the security tape but the other player said to me that if we just split it he would do that once we determined what was in the pot he said just give me $55 and call it even so I did.
Your first point is something I've never come across. Once a hand is mucked it's mucked and I've never been told I need to keep them in any kind of order that would allow the players to have their cards back in the event of a dispute.
You keep the burn cards separate (typically with the pot) until the end of the hand to verify that they are indeed all there, but once the hand's over you muck the lot into one pile and shuffle the next hand - there's no order or anything to it. Plus the amount of time between when you bring the deck together and when you start shuffling the next hand is under a second, so I'm really not sure what benefit it'd have anyway. Be interested to hear where that one came from.
And on the second point, that's just weird. He turned his cards up, you didn't look at them, and then
chose to believe it when someone else said he had a straight? No offence, but if I had to pick the most likely scenario there I'd say he had 4-2 or something, the other player misread his exposed hand and then your villain decided to go along with it when the comment was made to see if he could get any money back. Or the other players were his friends. Either way, I'd say you got rolled there.
Anyone who's hanging onto 5-2, gets to the river on that board and then bets
knows whether they've got a straight or not.