<p>I want to create parts for a 3D printer using OpenSCAD. Having some STL files from the vendor, but nothing else (no technical drawing, no CAD files).</p>

<p>Does anybody knows a free tool, that allows me to</p>

<ul>
<li>measure distances between 2 selected vertices,</li>
<li>measure distances between a selected vertex and a plane defined by 3 vertices,</li>
<li>measure the radio of a circle defined by 3 selected vertices?</li>
</ul>

<p>I very much like the way Blender allows to work with meshes, especially select vertices or planes, but unfortunately haven't found a way to measure with Blender.</p>

I suggest Blender. It's not the simplest of tools but it is free and learning it will improve your 3D printing skills. :-) (I write this answer also for future viewers of this question so I start basic).
Another answer can be found here,
How do I measure a distance between two points?
Import your STL file.
Press the Home key to view everything.
Select the model by clicking on it with your left mouse button. (Blender changed to left-click-select as of version 2.80)
Hit tab to enter edit-mode.
Press N (or use View | Properties) until the Properties panel shows up.
Select the "Length" checkbox in the "Edge Info" section of the Properties panel (see image below).
Select "Edge Select" mode (see image below)
Select the edge to measure by clicking on it with your right mouse button.
If you need to measure the distance between to vertices with no edge. Create the edge by selecting them and pressing
F
.
If you need to measure the distance between a vertex and any other point, select it and press
E
to extrude.