Does collective security threaten a country's sovereignty?
I would say both yes and no, and lean more towards the "no" side. Certainly, submitting to the majority will of a foreign body, or to the particular requirements of a treaty is a form of surrendering sovereignty. However, it's a pretty limited and conditional surrender. It's not as if by being in NATO or the United Nations, we lose the ability to pass budgets, or control traffic, or legalize gay marriage. The vast majority of our sovereignty, and the part, to me, that really matters, remains intact.
I could also argue that while, if one NATO nation is attacked, the US is legally obligated to go to war on their behalf, that same arrangement also protects us. If our physical sovereignty is ever threatened, we have protection, which makes that sovereignty actually stronger.
In theory, it certainly does. That is, for example, a major part of the reason why the US Senate did not ratify the Treaty of Versailles that would have put the US in the League of Nations.
Under the principles of collective security, a country does not have the right to decide when it goes to war and when it does not. If one of the countries covered by the collective security guarantee is attacked, the other countries must defend it. In this way, they have given up their ability to choose for themselves (and thus their sovereignty).