Recently, a new rule has been added which disallows rotating a player's view. (https://www.speedrun.com/mcce/thread/7smxx) On rare occurrences when spawning into a village, a villager spawns next to you and he might push you from your spawn point by about 1-2 blocks. If this happens, would the run still be accepted, or does it make the run invalid?

i had this happen with the drowning zombie dudes in my find emerald seed, i imagine the time would start when you get pushed but dunno if there's any rules on that yet

Time would probably start upon being pushed, yes. Depending on the exact circumstances of the run it might start earlier.