Is there a way for a non-US resident to find out if there are
outstanding warrants against him, before he enters the USA?
The United States does not have a unified court system and as a result does not have a unified court records system.
One would have to independently search the court records in every U.S. county (about 3,000) and every U.S. municipality with a municipal court (on the order of 10,000), plus each of the federal trial courts including District of Columbia and territorial courts (about 100). Many of these would have to be searched separately although some states have unified state court records which sometimes do and sometimes do not include municipal courts. And, by the time you did all of those searches, some of your earliest search results would be outdated.
Importantly, the authority to issue arrest warrants is not limited to criminal cases. An arrest warrant can also issue, for example, for failure to appear pursuant to a subpoena or a contempt citation that has been personally served upon the individual named in the arrest warrant. Thus, arrest warrants can issue in almost any kind of case.
There are databases of outstanding warrants that are used for background checks and by law enforcement, but the databases are not comprehensive, are not always kept up to date in a timely fashion, and are not authoritative and official records. Typically, a positive hit would have to be confirmed with an official court record, while a false negative might happen on the order of 5%-30% of the time before even considering arrest warrants issued under seal.
In practice, this is less of a practical problem than it seems, because the vast majority of arrest warrants are issued for defendants who reside in the arrest warrant issuing jurisdiction, because most people commit crimes where they live. But, it is impossible to get a guaranteed answer that there are no outstanding arrest warrant against someone.
A key limiting factor, however, is that state and local arrest warrants are can only be served within the state where they are issued, in the absence of an extradition request approved by a state governor (and only allowed for certain crimes), an international extradition request, or certain kinds of INTERPOL warrants. So, something like 99% of arrest warrants can only be carried out in the state where they are issued.
If a non-U.S. resident knows which states he will enter within the U.S. on his trip (e.g. if he knows that he will only be visiting Hawaii and California, or will only be visiting New York State), the number of jurisdictions that can be searched to get a definitive result is much smaller and the accuracy of a database of that particular state's outstanding warrants will often be much more accurate than it would be in a national search.
But, any state or local arrest warrant issued by any court in a particular state, such as Colorado, can generally be served anywhere within the state, not just in the county or municipality in which the trial court in question is located.
I am not familiar with the law governing where arrest warrants issued by federal trial courts can be served, but these warrants make up only a tiny share of the total number of warrants outstanding at any given time, although they may have special relevance in international cases as cases involving non-residents of the U.S. are much more likely to be in federal court than other cases.
Are authorities obliged to inform any defendant anywhere in the world
once a warrant is issued?
Generally speaking advanced notice of an arrest warrant is not required and an arrest warrant are issued ex parte (i.e. without an adversarial process).
Arrest warrants can be, but aren't always or even usually, issued under seal, so usually (but not always) a public records search will disclose outstanding warrants in the jurisdiction searched.
Can a potential defendant request this information?
But, if the arrest warrant is issued under seal as it sometimes is (particularly in organized crime and gang cases), a public official receiving such a request would not reveal its existence of the warrant.