Because lots of people are drawn to the internet. She had a Facebook account. I've been in countless settings where a laptop is rarely idle around a small group of young people.
Doubt she was searching his personal computer files. More likely she Googled his name while he was out getting coffee and bread. Her family did exactly that when provided the name "Joran van der Sloot" while Stephany was still missing.
I doubt she was even on the computer. I think he was lying about that whole thing. Why would he ever have information in an email about a murder he committed?
Serial killers are psychopathic, not stupid. (they also lie)
I doubt she was on his computer. He probably has it password protected. This albi might have held up if she had her clothes on.