Most likely, you hit your other Timer0. Most people have an alternate Timer0, which adjusts the frames. If you can't locate the frame you landed on, that's most likely the problem. Simply try again.
Since you can't really tell if/when the NPC moves, you can't tell how many advancements it does. If you want to go less Chatot advancements, try, but obviously adjust if you don't get the right one.
Nope. Once you pick up the egg, the IVs and nature are set. So if it ends up being the wrong one, simply reset and redo everything again, adjusting if needed.
Got it. If you've done everything correctly, then yes, your starting PID is 53. So now, reset your game, do your RNG process the same way, and this time, before you pick up the egg, go to the Pokemon Party menu and listen to Chatot 73 times; since you're starting PID is 53 and your goal is 126, that's how many times you have to listen to Chatot to advance the PID frame.