Providing false information to WordPress is probably not legal.

This is what I had in mind; good old CFAA. Ditto for entering false info in moneygram. (Not commenting on whether these things should be illegal.)

Well, it also touches on fraud and impersonation, old, long established crimes, not just computer hacking.

Is laundering legal money and then using it for legal purposes illegal?

If the money was obtained legally to begin with, concealing the source is not illegal.

http://www.law.cornell.edu/uscode/text/18/1957

If the laundering method is illegal, then yes.