The Diavolino itself does not fit on a breadboard (it’s too wide), but you can fit small breadboards on top of the Diavolino. (For example, on a Googly Shield: http://evilmadscience.com/productsmenu/tinykitlist/438-googly ) However, it is definitely possible to wire up many things from the Diavolino to breadboards.
The Diavolino itself uses much, much less power than USB can supply. USB can normally supply up to 500 mA, and the Diavolino itself never draws more than 1/10 of that. But, you can hook things up to the Diavolino that would draw much more than the computer can source. So, your computer may have been right, but it depends what you had hooked up, and where and how.