Dirk-Jan,
First, make sure you know the difference between a text box (first blue icon from the left) and an input box (second blue icon).
The text box is for explaining what has to be entered into the input boxes, and they are usually placed to the left of the input boxes, or above them. The actual text has to be entered in the 'tool area' on the right side where it says 'Your text', and as default it has 'Your text here' written in it.
The input box has to have a name/label since you are likely to have several input boxes and you need to see what they are when a filled-in form comes in by mail. You write in the Name field in the tool area something like 'firstname' or 'birthplace' or whatever is needed. The name/label is not visible in the form while working on it, nor is it visible in the finished form.
The input box also has an option where you can use a 'Starting text' in addition to, or instead of the text box that I've been banging on about above here. If you write a starting text for your input boxes, that text can be removed by the user who then types in whatever information you are asking. The starting text is not visible while working on the form, but it is visible in preview and in the finished form.
I was not able to open your first attached screenshot (you can see it has 0 Bytes), but from the second screenshot it looks like you have confused the starting text with the text box. You know of course, that the box you want to work with has to be selected, and the tools on the right change according to which element you have selected.