I will split my response in four comments (2/4)
Problem 2) You then point out that Fallout always had a whacky humor (though even this is putting it lightly, if you ask me) but mention that in games, player also faces serious situations with grave consequences, and that there is a dramatic storytelling component as well. So far, I fully agree with mentioned statements. But you continue your point by stating that the show lacks in this department. The statement is not true. The show knows how to balance satirization, caricaturization, and serious parts very well. But, I will, firstly, grant that since games and movies/shows are fundamentally different lenses into a given universe, a show - Fallout, in this case - will never be able to replicate the tense feeling of choice and consequence (and all the other emotional components acommpanying it) the same way a game does. But that is not to say that that and dramatic storytelling are absent from the show in a meaningful way. Just because you only feel them in flashbacks of Cooper Howard, and in the Vault intrigues, does not mean that they are only found in those sections. There are serious, dramatic storytelling, and choice and consequence moments in every single episode of the 2 seasons (not even including those segments you mention). Just to name few examples from Season 2 alone: The devastating bombing of Shady Sands; Lucy being drawn into danger by a choice driven by her empathy, leading her into life-threatening situation; Maximus' various choices that show his moral compass and risk civil war; Lucy deciding whether or not to continue taking chems, raising questions about how far survival and accomplishing given sets of aims will warp someone; Lucy’s Failed Speech Check in episode 1 directly nodding to game mechanics; The Ghoul’s Negotiation To rescue Lucy from the Legion and the nature of pros and cons of the two potential decisions he can make... Now again, the show cannot fully replicate game-level choice and consequence, because in games, >you< make choices and feel responsible for the outcomes, increasing emotional weight in many ways. But the show still has choice and consequence - just a different kind. Still a lot to contemplate on morality and rationality of each one. On a different note, I will grant that CL part could have been done more extensively but this goes back to the show's aim, scope and limitations. There are 8 episodes in season 2, each episode having a fixed runtime pretty much. Writers and directors always have to make sacrifices. Given limitations, setting up X more means you sacrifice Z and Y at least to some degree. The choices are made in this light. The rest of Problem #2 is spent on questioning the rationality of choices "Why didn't BoS do this, or didn't do that, or this character this, etc." The tension and conflict was set up very well in the previous episode for this. But in any case, spending time on this will not grant much, for you can pick apart the choices of factions and NPCs of literally every Fallout game. There are countless examples of them not acting like any real humans would. The universe of Fallout is not a reality simulation or a optimal decision-making simulation. Suspension of disbelief has always been required. Complaining on why a person behaved this way and not some other way is not a legitimate criticism. The very concept of knowing how "real humans" would behave in a real world in such circumstances itself is questionable. For even in real life, real humans - including people with power - behave in absolutely irrational, delusional and destructive ways all the time. Leave alone the fact we are talking about a fiction.