1. so my understanding is that they determined that the yellow flag was displayed so briefly (because he pretty much immediately left the sector and his dash went green again) that he effectively didn't have time to react. the decision document also mentions that his attention in that moment was on his mirrors because he was anticipating needing to defend against Max, which makes it even harder to expect him to react in such a small amount of time. by the time he looked up to see the yellow it would have already been going green again
2. apparently the rule (and I heard this confirmed by a lot of credible people) is that after they let the cars unlap themselves, there then has to be another full lap under the safety car. so since they didn't do the unlapping until lap 51, lap 52 had to be under the safety car. cue lots of confusion since this rule obviously wasn't followed in Abu Dhabi 2021 lol
3. I will try not to let this answer be colored too much by Kimi haterism lol, and this is mostly speculation. when the car started having issues, Bono kept asking for more information from Kimi and Kimi was just kind of floundering. so part of me wonders if the panic on Kimi's end contributed to the confusion and delay in figuring it out. and as much as I would love to give George credit for being a genius and immediately calling it out on a replay, part of me suspects that someone mentioned something to him about it in the interim that clued him in or at least gave him a hint about what he was looking for. incidentally the live broadcast was showing Kimi's onboard at the moment it broke. when I rewatched the race with my friend later in the day it became obvious when it happened but only because I knew to look for it, the first time around I didn't clock anything amiss at all
1. what was the yellow flag infringement from lewis and why didn't he get a penalty for it?: I get what the stewards are saying, but I don't think Hamilton would've gotten off this easy if he weren't a 7 time world champ. I've read a bit about it and the whole "Lewis was watching Max in his mirrors" isn't a real excuse. Any other driver would still get penalized, are they now able to also use that excuse to get out of a penalty as well? and ironically, Max himself had already seen the yellow and backed off, so Lewis should've noticed Max slowing down too. i understand he had no warning going into the sector at Turn 9 and that's on the software, not him, and he shouldn't be penalized for that part. but by Turn 10, the stewards confirmed the yellow was on his dash and the panel was lit, and he still didn't slow down. That's no longer a software issue, that's him not paying attention. If he'd slowed down the moment the panel/dash showed the flag, I'd have been fine with no penalty or just a reprimand. But he didn't, and failing to react to a yellow flag is a safety issue that should carry a real penalty, not just a reprimand tbh.
2. why did they finish the race under a safety car?: That makes total sense! it just doesn't make sense how on my broadcast and afterwards during briefing, no one had a clue about this rule. maybe it is because as you say it didn't happen in abu dhabi '21 which was a whole other disaster, so that makes sense. i also think it makes sense they wanted to lap the cars but it was honestly a shame tho as we didn't see any racing anymore.
3. does anyone know why Mercedes took so long to figure out what was wrong with kimi's car?
honestly don't wanna sound a kimi hater either, but when i watched the first thing i clocked which really annoyed me was kimi freaking out. i understand from his pov but as you mentioned it definitely didn't help and i felt like bono was also getting fed up with it, as was i. obviously he was panicking but i feel like if he just for a second listened to bono and the team they could've figured it out sooner. instead he just went driving around like a lunatic who could barely control his car and went off multiple times which honestly was a danger to passing drivers. ngl i also didn't notice, i did think it was a bit weird how there's so many and no one saw but then again it could be possible they didn't even look at any of the broadcast but instead at their system and that didn't flag anything so that would make sense as to why they didn't clock it. lol, wouldn't be surprised about the george part, 100% something he would do haha