Hello
Ice Cold, I'll try to satisfy your queries to the best of my abilities, as I'm sure some others will aswell
Fireweapons, flamers etc, could have been preserved along with many other weapons, in FO3 there are quite a few armouries and caches dedicated to the safehousing of weaponry of all kinds. Naturally, all the weapons of the world weren't laid out on the turf waiting for the bombs to be dropped. Most of the weapons you will see ingame will have been looted some way or another. Some flame units may have been damaged beyond repair, and stripped to be used in other weapons of the same type.
Some people could have used any makeshift shelter to survive. The most harmful aspect of the bombings would have been the radiation in the first few years after, the bombs themselves wouldn't have caused alot of damage, the aftermath would have been the real testament to survival, hence the ghouls you see. Also none of the games are set directly after the bombings, so the civilisation you see out in the wastes would be a second generation. Vaults kept people uncontaminated and safe, but there was always a chance people outside would make their own go at survival.
Behemoths are an unknown. Personally I don't agree with this deicision by Bethesda, Mutants know enough to dip people in F.E.V to mutate them. The closest thing to a Behemoth in previous games would be Frank Horrigan from FO2, and he was the result of many experiements by the Enclave's science team. Mutants wouldn't possess the intelligence or the means to provide the necessary experimentation involved in creating these gargantuans. Maybe they were enclave experiments, but it wouldn't add up. Personally I just think Bethesda wanted a big bad monster, and logic didn't come into it.
There are 122 Vault-Tec Vaults. Only 17 of them were designed to work to public expectation. Vault 8 in FO2 is the result of such a working Vault. The rest were experimental Vaults. The outcome of most are still unknown, it would be safe to put most of them down to fan speculation until developers decide to include them in-game.
Nuka-Cola was a very big distributor before the great war, and bottle caps were just the answer to currency due to their abundance, there is no 'real' reason for it, it just gives you a good impression that civilisation has been destabilised. It's more an aesthetic than anything, bottlecaps were the currency in FO1, in FO2 it was coins (civilisation began to pick itself up after 80 years it seems), and Bethesda decided to bring bottlecaps back for FO3 200+ years after the bombings, so you draw your own conclusions.
Maybe someone else would be able to provide a little more flavour, but I'll try to be as subjective as I can