The US doesn't need a 'secret warrant' to ask for information from another country. They don't really need a warrant at all. They just ask for it. IIRC, even the NSA isn't legally bound to avoid spying on American citizens when they are out of the country.
To avoid it, no. But if they do uncover evidence on American citizens it could not be used in a trial and must be filtered out (although, see 'parallel construction').
