That is not true. State courts can apply foreign state laws, and federal courts can apply any state’s laws.
Again that seems needlessly pedantic. Has there ever been a case where a court applied a law from a regime where that regime's own courts lack jurisdiction? Again, in practice "laws apply" and "courts have jurisdiction" are isomorphic states. Complaining about an article making the very reasonable conflation seems nitpicky and silly.
Sort of yes, sort of no.
For example, imagine an American tourist visiting the UK drives dangerously and kills a motorcyclist, then escapes to the US before being caught.
A UK criminal court can order jail and a driving ban, but has no way to enforce the sentence unless the tourist decides to return to the UK, or the US decides to extradite.
A US criminal court can't do anything, the crime took place outside of their jurisdiction.
The victim's family can sue the tourist in a US civil court, and that court can take UK law into account - but can basically only impose a cash settlement that gets paid out of the tourist's insurance. They don't actually lose a cent.
So in a sense one state's courts can apply foreign state laws. But in terms of results, i.e. days spent in jail, laws don't appear to apply across borders.