US law is clear, especially after the Salinger case: you cannot reprint a letter without the writer’s permission. It is a copyright violation.
Actually, the US is one of the few nations where copyright registration is needed. Most other are full signatories of the Berne Convention, which does not require registration.
Here is a list of countries that are signatories to the Berne Convention. Note that if they are signatories, copyright does not require any registration.
Yes it is – but you need to explicitly give that permission. Most professional publishers send out contracts spelling out what rights they are buying so there’s no question. There are some exceptions, such as letters to the editor, where there is a reasonable expectation on the part of the sender that the letter will be published. However, a private e-mail does not fall under this.
Note that the author can make as many copies as he wants, but still retains copyright unless he specifically says the work is in the public domain. Copyright is, after all the right to make copies, and if the author has the copyright, then he can make copies all he wants.
If you want to look through US copyright law, it’s at http://www.copyright.gov/. But you would win any case if you registered the copyright and cared to pursue it (though, more likely, the other guy will offer to settle out of court, since he has no way to win).