1.) Once the players encounter something, it is locked. I do not change the abilities of a monster, the mechanics of a magic item, or the mechanics of a spell. I only violate this rule in cases of grevious balance issues, and I have encountered none of those in 3E, 4E or 5E official official RAW. I have tweaked a couple homebrew things I initially allowed, but not RAW.
Same. I only change something after it has been encountered if it's broken somehow, and then I let the player know why I'm changing it.
2.) As a DM, I do not fudge die rolls. Ever. The dice giveth, and the dice taketh away. I am willing to let PCs die due to die luck. I tend to not end a character story when the PC dies, but instead continue to have the backstory elements of the game impact the setting, keeping the PC 'alive' in the story even as the player runs a new character and we add other elements to support the new PC. To that end, death is just a step in the story - and I know that a PC's death gives that story closure, which is often preferable to the campaigns that stop mid-way through a PC's story and leave their stories unresolved.
As I said, I only do it for extreme bad luck and not just bad luck.
As an example, my last campaign was set in Ravenloft. Early on, I want to say around 3rd level, the party encountered a Banshee. She screamed and bad luck hit. Three of the four PCs failed the low save and were reduced to 0. Only the Barbarian made the save. Fortunately he was a beat stick and drove her off, but not before one of the PCs failed three saves. More bad luck, but not extreme. That's just normal game play. 1 PC dead.
Later on the party encountered some Sons of Kyuss. The PCs dutifully scraped off worms that hit them every round, until one round where the player of the PC that died to the banshee decided he wasn't going to scrape off the worm and just attack one of the monsters. Worm burrows and a second dead PC later, he said that he probably shouldn't have done that. Bad decision and a PC death.
Later on in the same campaign, and I can't remember the last campaign where three PCs died, the player of the Barbarian stayed behind to look for an invisible creature that had just given the entire party a hard time and then left to find easier pickings. The creature that hadn't gone far noticed this and then killed the Barbarian, despite the Barbarian getting very lucky with his dice and almost killing it. Another bad decision and another PC death.
In the current campaign I have had one PC death so far, also due to poor choices on the part of the group. Death is very real in my games and since I make raises hard to get, usually permanent.
As a player, I will occasionally decide to fail a roll. I do this because it makes the story of the game better. This is more common with inexperienced DMs that are not as prepared to handle a novel solutionto a problem. Usually, this is above the board ("I rolled a 17 for a total of 26, but I think it'd be more fun if I had rolled a 3 and had a total of 12. Can we say that happened?"), but I have on occasion done it without revealing that I was being deceitful about the dice when I felt like it was really necessary, and when the discussion of it might not go over so well.
I've failed rolls intentionally and had players do it in my game. Usually not after the roll, though. Normally the player just opts not to roll and fail.