It's not an entity of the Netherlands government in any respect.

As far as the actual country of Netherlands goes, the United States and that country have a standard extradition treaty, as the US does with most countries that have a reasonable court system that protects the rights of the accused.

The US views the ICC as an illegitimate kangaroo court that does not meet the minimum standards for such protection, and thus does not recognize it any more than it would recognize, say, a terrorist-run "Islamic court". If such "courts" grab US citizens and put them "on trial", then, yeah, they shouldn't be surprised when US Navy SEALs coming crashing through their windows. That wouldn't make it an "invasion" of the country where the "court" was located, but something more akin to a hostage rescue mission.

No, it doesn't, which is why it makes referrals to the ICC. The US just believes that the US, uniquely, should not be subject to any external accountability, because it uniquely can be trusted to hold its own war criminals accountable without such external fallback.

Yes, actually, it does.

https://2001-2009.state.gov/t/pm/rls/fs/23428.htm

In part: "We object, however, to the investigation or prosecution of our citizens by the ICC, whose jurisdiction we have not consented to and which lacks necessary safeguards to ensure against politically motivated investigations and prosecutions."

Read the whole thing.