Thinking about the first episode again - if they trade with the other vault every 3 years (triennial I think?) how do they not recognise that everyone from the vault are people they've never met before? Like it doesn't make any sense.
Very few things about the first episode make much sense, the moronic three-vault system and Moldaver's invasion plan in particular, and some of the implications are downright insulting for the audience's intelligence. I can't answer your question but I can offer even more questions to ponder for fun.
Why does not a single one of the Vault 31 immigrants living in 33, people who are supposed to come from Vault-tech's junior management staff from 2077 recognize Moldaver, who in 2077 was a public figure, their main detractor and the person responsible for the stupid cold fusion gizmo that Vault tech bought? On that note, since we know that every single Overseer comes from 31, how the fuck an Overseer not from 31 suddenly appearing did not raise an immediate alarm?
When a wedding arrangement is made from 32, the overseer and a bunch of randoms are invited for a celebration, what the fuck happens when a new citizen from 31 like Stephanie for example comes over? They arrive alone or do they defrost all the remaining Vault tech executives to have a little cake and return to stasis? Nobody notices that it's always the same people, always staying at the same age?
Why the flying fuck does Moldaver come with a bunch of almost feral, barely human raiders who look and act like extras from an Italian Mad Max rip-off when we later know that she works with (and maybe is the leader of) a big group of ex-NCR citizens? Why, Jesus, why do they have to wait until the wedding is consummated and Lucy, our plucky protagonist, is raped by deception? (I know the answer to both those questions is "so we can have a nice slow-mo action scene with 50s tunes in the first episode" but you know what I mean).
Some of those can be somehow hand-waved, and I'm pretty sure people are already building head-canon to desperately fix the holes, but it would require a truly exceptional set of coincidence and unlikely events to do so with all of them; the plot is broken beyond repair at this point.
The logic of this show dissolves like a sugar cube in a bucket of water once the "mystery boxes" are opened, in a spectacular way usually reserved to the later seasons of shows where people like J.J Abrahams or Lindelof are involved. At least in those case audiences get a few seasons of blissful ignorance and naive speculation until the ugly truth that the writers made everything up as they went along and didn't give a single fuck is revealed as some sort of meta plot-twist.
And how are there fat people in the vault with limited amounts of food?
This one I can answer, tho. Despite the Vault having a minuscule plot of land to feed maybe a family of six (this is a nitpick for humor purposes, a small plot of land is visual shorthand enough to communicate that they do indeed farm, specially in a show like this), most of the food we see them consume looks like it was prepared with heavily pre-processed pre-war ingredients, like canned meat, jello, ice cream, cakes and the like, and even in Vault 4 people are still eating Sugar Bombs and drinking Nuka Cola and giving them away to the first dumbfuck who happens to pass by. In fact, the food that Lucy takes for her aimless search of her father looks more like what one would find rotting in the shelves of a Fallout 3 supermarket and not in a vault, but references are more important than logic in this show. The real question is how are there thin people in a vault whose diet consists on 95% junk food and 5% corn.
Compare and contrast Fallout's 3 intro, where having a medium-sized birthday cake for 20 people and a sweet roll for yourself is seen as a luxury reserved for important occasions with the show where they feed giant elaborate cakes to a bunch of murderous bastards.
(Cooper Howard) after himself, BTW. Maybe it's prophetic.
