No, the USA would not survive a global war versus every other power. The US has enough missile subs, secret launch bases, and distributed silos to make it impossible to do a joint strike to eliminate the entire American nuclear arsenal. But very few would survive that war - most of the planet would be an irradiated uninhabitable wasteland. I would expect you would have survivors of a global nuclear war, but it would not be a pleasant world to live in.

There is no situation where you could do a ground invasion and takeover of any sufficiently nuclear armed first world country where that country would not use nukes as a final measure. That is what they are for. I mean go ahead, try taking over Pakistan and see if they don't nuke you for it, for example.

Like Ukraine's nuclear weapons protected it from Russia ?

Here is a clue. As the world situation changed, Ukraine lost its nuclear weapons. Want to bet that will NEVER happen to the USA or the successor of the USA ?