As far as I know, most real Nazis emigrated after the war to flee the "Entnazifizierung" (de-nazification). Many of them went to Chile and Argentinia, but a lot of them also got false papers and went to the US. And many members of the scientific elite of the Nazi science projects actively were recruited (and subsequently pardoned by your Government) by the US.
It is not your country but ours you could be fined or even (depending on the severity of the case) for displaying Nazi symbols like the svastika or the Double-S-Runes, the Uniforms, the Flags or even for uttering the "Heil Hitler"-Phrase in public. Yes, there's still a couple of brainless nationalistic skinheads over there. But that holds true for many countries, including Russia and the US. The difference is - here those guys are not allowed to have weapons and go to jail for it.
As for the american natives eradicated: at the arrival of the first spaniards, french and british colonists the estimated population of the americas was about 90 million, in North America roughly 40 million. The active casualties of war since the declaration of independence in the US alone is roughly 1 million, with another 20 million deaths by disease (very often actively spread, e.g. by pox-contaminated horse blankets issued by the military in the various reservations) or malnutrition and cold (in said reservations - essential the worst pieces of therir own former country - so bad, nothing of worth grew in there, so no settler ever wanted it. And wich they were forbidden to leave well up into the mid-1900s.
It is not "several centuries ago" - the Wounded Knee was a mere 40 years before the rise of the Nazis, the Pine Ridge shootout (the FBI shoting protesting citizens of the AIM) happened in 1973. And the Reservations - well they exist up to today.
As for the protection of our country - we are thankful for the protection provided in the cold war (even if we are acutely aware of the fact that both sides of Germany have been planned to be "burned ground" by both sides of the big cold war -fractions from the very first day).
We are thankful of the destruction of the Nazi-Regime by the Allied forces - but there is no protection of our country by you today, because there's simply no aggressor to be protected of.
As for overthrowing the world - most countries leave that to the US nowadays and keep to the clean-up, after the US troops have marched through yet another country and the Burger Chains and Coke start to settle in.