Ah, I was just about to say the same thing. I sometimes plug my other external drive into it with no problems. So yeah, there's that option. There's also a 2tb version, just in case you have mad on for extra space
Cookies are just text files so even if you run out of battery they're still there like any other file.
Unless the sites in question are only storing the data info in session (ie as long as the browser is open and you're on the site), which would then dissapear if you shutdown/close...