I've been working on the problem, couldn't do much about the connection since it was working fine. So I re-created tables for Orders and Order Details in my MySQL detabase, to see if it would make any difference. Not really sure if this was one to make actuall difference, but after I tried Checkout Wizard again, this time worked!
Sorry for the trouble, these days this happens a lot: I was so desparate so I ask you guys, then I ended up solving problems!
I don't mean to swing you around, really!