I've seen a reference to the callsign A7RW. I can't find it in the FCC database or by searching the ARRL. Is it a legitimate US callsign?
A7RW would be the call sign of a ham in Qatar, rather than the United States. The prefixes AA – AL are allocated to the United States. So AA7RW, AB7RW, AC7RW, etc. up to AL7RW would be valid US call signs.
The FCC have certain call signs that they won't issue, like a call sign with a three-letter suffix starting with X (so I heard, can't find a source), such as AA7XWW. I don't know that such a call sign could be called "illegal" though, because the rule might not be codified into law. The FCC issues all call signs, so they could simply refuse a request for such a vanity call sign according to an internal rule that hasn't been publicized or made law.