Yep, it's true. And yep, it's old. You use the same wireless internet as you do fo the games. It works pretty much the same as a normal web browser, the control stick moves the mouse, L and R work as back and forward, and you enter the address the same way you type things at other points in the PSP. It's even got cookies and remembers where you've been in a history thing, just like on a computer. Plus, you can conveniently go to a menu and delete the cookies and such in an instant.
Yes.You use the same exact typing thing you use on the other parts of the PSP. Just select a text box, and you can type in it. Actually, I once made a post on here with a PSP, so I know for sure it works.