Sorry, but if the documentation of a free program has FDL, then it can contain invariant sections, so that I am limited :)
Wrong. Only if it _has_ invariants.
No. I'm limited because someone can insert invariant sections later, a newly modified derivation. I can't reuse that derived version without taking the invariant section with it. :-)
You can't take a GPLed licensed work without licensing the derived work under the same terms as the GPL. So you cannot reuse the resulting work under a GPL-incompatible license.
But you can reuse parts of the work under a GPL-compatible license. And it's up to you which parts you take.
You can't reuse a non-GPL compatible work with a GPL licensed work, I fail to see the point. If they are incompatible, well, then they are incompatible. This doesn't change the freeness of the license.
Nothing different for the GFDL.
Quite different for the GFDL. You can reuse parts of the work under a GFDL-compatible license, and you can choose which parts of the non-invariant sections you take, but you always have to take all of the invariant sections.
Not different at all. With GPLed compatible works you need to take the copyright list, if the extra inclusion of some text is so annoying to you, don't use the work. It still doesn't change the fact that the GFDL is a free documentation license.