Hmm, those are pretty strange errors

I never heard of those kind of problems and for example the first error: there would be a lot of people complaining about this, but you are the first one. So I think it's a problem with your server configuration, some mods to the DownloadsII code, or something custom like that.
Have you installed the newest version of DownloadsII (5.0.4 at the moment of speaking)? Cause your postbit info says to me that you didn't download it ever, which is pretty strange. Maybe you have the old ecDownloads of Ron1n installed (which we don't support, you need to upgrade to DownloadsII 5.0.4)?
Is there anything special you can say? Like mods to the templates, plugins, normal PHP code, ...? Or a special server software configuration?
Btw: if you can pm me the user info of a normal user test account with upload and comments permissions for DownloadsII, I can check it out for you.