Is there any way to see if people have tried to get to non-existing domains? I mean, if someone requests doda.org and it does not exist, is the request logged anywhere?

The only ones to know about that request would be one of authoritative nameservers for "org." (which happens to be the A-K root nameservers). Would they log it? Almost assuredly not (at least not in a log that they would keep for very long). It would be just another request for an undefined domain. Tony Rall