I don't know the laws for photos, but as someone who does writing, I do know that material is considered automatically copyrighted from the moment it is completed. Technically, I believe that the person who creates the files has ownership, which means the rights to share or not share on their own terms.
I suspect that the e.mails belong to the person who wrote them, saved them, and stored them in his own computer. I could be wrong (which, of course, doesn't answer your question - sorry).
I suppose, technically, the matter is not about using the computer or invading privacy since the friend gave permission to "full use" of the computer. Maybe some law would say that without specifying what is meant my "full use" copying files may not be legal. On the other hand, some law could say that "full use" doesn't include copying material.
I'm not entirely positive that what your boyfriend did was illegal (although it could very well be). I think, though, it's more a matter of taking liberties after being given permission to use the computer. This is one of those situations - let's face it - when most people would assume that "full use" means checking e.mail, going online, typing a paper, etc. - not copying the contents found on the PC. Legal or not, your boyfriend took a liberty that the friend probably never would have imagined would be taken. (I know when my son comes to my house and uses my PC here I wouldn't imagine he'd copy my files without asking.)
There may be a law that says a person has a reasonable right to expect that the files on his computer will be treated as personal property, and a person (even one who lets someone use the PC) has a "reasonable expectation" that files will not be copied. Then again, maybe there's a law that says that by allowing anyone to use your computer you have given up your rights to such an expectation.
I think your boyfriend could help the situation by telling the friend, "Hey, I'm sorry. I just assumed it would be ok if I copied the files. It didn't occur to me that you'd mind. Now I know differently." Sometimes it isn't a matter of what's legal or not, but a matter of a misunderstanding between two people who have different expectations of what is private and personal and what isn't. The friend probably feels he "gave your boyfriend and inch and your boyfriend took a mile". He probably trusted your boyfriend to just use the machine and is probably feeling he trusted him more than he should.
An apology and an offer to delete any copied files from your boyfriend could go a long way. Sometimes if someone just acknowledges that he did cross a line (at least in the eyes of some people) it can make the "wronged" person feel less "victimized". Maybe it can't be called an "intrustion of privacy", but I think it could be called a "betrayal of implied trust". :)