I assume this would go here, sooo I know many of the vaults were designed for experiments and such. Now I'm assuming the government in Fallout also had the belief that you could win a nuclear war or suffers acceptable losses. If this is true, then that would explain why Vault-Tec ran the experiments. Or is it possible Vault-Tec and even the government did not really believe the war would occur.
If there is no belief that the war would end in America's favor why would Vault-Tec even run the experiments?

Sounds like your confusing Fallout with Earth 21509, the Enclave is simply the remains the of the american goverment. In Fallout 2 the Enclave was working to wipe any and all mutations, and restore america, which seems to be the case in Fallout 3 as well. Vault-Tec on the other seems to have been a powerful corporation with many goverment contracts. Their experimentation seems to have been an effort to expand weapons development. Thing is, did Vault-Tec merge with the Enclave after the war, or was Vault-tec a goverment front.

Sounds like your confusing Fallout with Earth 21509, the Enclave is simply the remains the of the american goverment. In Fallout 2 the Enclave was working to wipe any and all mutations, and restore america, which seems to be the case in Fallout 3 as well. Vault-Tec on the other seems to have been a powerful corporation with many goverment contracts. Their experimentation seems to have been an effort to expand weapons development. Thing is, did Vault-Tec merge with the Enclave after the war, or was Vault-tec a goverment front.

Officially, the Vaults were nuclear shelters designed to protect the American population from nuclear holocaust. However, with a population of almost 400 million by 2077, the U.S. would need nearly 400,000 Vaults the size of Vault 13, while Vault-Tec was commissioned to build only 122 such Vaults. The real reason for the existence of these Vaults was to study pre-selected segments of the population to see how they react to the stresses of isolationism and how successfully they re-colonize Earth after the Vault opens.

The shadow government, the Enclave, responsible for the experiment, have considered themselves prime candidates for recolonizing the world after a nuclear holocaust and to this end commissioned the construction of their own shelters, isolated from the Vault network. The purpose of the Vault experiments was to help prepare the Enclave for either re-colonizing Earth or colonizing another planet if Earth turned out to be uninhabitable by unmutated humans.

The total number of vaults is a government secret and has been lost; there were the aforementioned "public" vaults, which numbered 122 and an undisclosed number of "private" vaults. Information on whether Vault-Tec was an international corporation and were there vaults made by them in other parts of the world, or were they strictly U.S. based, cannot be released due to Vault-Tec and US Government regulations[1]

Your information may or may not be valid to answer some questions.

In any case, that would imply that the government actually thought they could win the war, and re-populate. Our own government did believe in acceptable losses. So why would the Fallout government be any different. And with the opening movie from Fallout 2 we have to assume the Enclave sees no purpose in the Vaults.

In any case Fallout 2 said the Enclave believed themselves to be the new american goverment, so there is no reason to believe that would change.

Is the spaceship thing official (from The Vault) or is it something somebody made up?

The Vault Systems were atleast in some part run by the government, and Enclave...In one of the terminals after you revisit 101, the overseer talks about how the Enclave attempted to get into the vaults using the standard password that they know about each vault. The Overseer wouldn't let them in even though they said they came in "peace"

So it means they atleast infiltrated the networks of Vault Tec...Or they just knew it from the get go.