I think it will be because you've moved them outside the <form>...</form> tags of the submit
Yes, i understand. I knew that already. Just wanted to show and explain the situation. You are right!
So, I compared with so called one page checkout from a 3rd party developer. There, all elements are ajaxified. It seems that I can move the things i mentioned to where i want them.
Question: Would it be possible for you or flexibledesign to add code or feature like this, in order to be able to move 1st and 2nd to a position above the basket?
I want to stay on this pure-theme. Because the whole theme is really great.
Thank you for your support John :)