The thing I am looking for is basically something like the diagram connectores (Ctrl+F2).
However, these seem to be pretty limited and seem only to be able to connect object centers.
I would like to connect two selectable nodes of two different objects and if I move them the rubber-bands will follow.
Is this somehow possible?

There does exist a new LPE (http://wiki.inkscape.org/wiki/index.php ... ttach_Path) that can do that.
Usage is not straightforward, though, so you may need to experiment a bit.

Generally you can get rubberband-like movement, by selecting certain nodes together, then they move together.

But I'm not clear what exactly you're doing. Could you explain it with a little more detail, or maybe even an a quick example?

Thanks @Moini, for the hint. Uhh, this is not intuitive and self-explaining at all . I need to spend more time on that.

Right, @brynn, if you select the nodes of the object you want to move plus the first nodes of the connecting lines/paths you get a kind of rubberband behaviour. I simply would move the objects around and don't want to bother about the linking/connecting lines, they should just follow like rubberbands.
I just want to have more flexibility than with the diagram connectors (Ctrl+F2). Maybe, I haven't understood completely how they should work.

Thanks again, @Moini, "LPE Attach Path" is the thing called I was looking for.
Indeed, as @Moini said, not easy to figure out how it works. I had the Stroke order: "Stroke,Fill,Marker" and was wondering why I get strage results. Apparently, in my case it needs "Fill, Stroke, Marker".
One example see below.
The idea to this example originally came from the post: viewtopic.php?f=5&t=31847
Where it was asked for partial visibility of objects or stacking order of "connected" objects.

As far as I remember, the Connector lines used to work like that - where if you move one of the boxes or circles (or whatever is being connected) and the lines/paths move along with it. I haven't tested it in some years though. As I recall, there were at least a couple of options for the style of the connection. The lines could touch or maybe even snap to....hmm....no it was before snapping was introduced, that's how long it's been since I've tested that tool! Anyway, the lines could touch the object, or stop some standard distance away from it, or be aligned to the center of the object (although the line itself didn't enter inside the object)

I remember some discussion, somewhere, and it was some years ago as I said, where Connector tool was being discussed. It sounded like a new version had resulted in bugs being introduced to the tool, which either had not been fixed, or the suspicion was whether the tool, which is not used much (in the opinions of whoever was discussing it) was worth fixing, or maybe should be dropped. But I don't remember who was discussing it.

I can't seem to get the first couple of buttons on the control bar to work. Although there might be some trick I either don't remember or haven't learned.

Oh I see. Ok, the lines do still follow the objects, if you move the objects. But they don't do it live. The connector lines only auto-adjust when I release the mouse button. It seems like I've seen a pref somewhere that makes the adjustment live, but I don't remember if it affects Connector tool or other tool.

Hhm, it seems like if you don't use the center connector handle to begin or end the connector line, and only connect the lines to the stroke of the objects, they won't follow the object when you move the object.

That's all I've got. The manual probably explains a few things.

I didn't realize you were talking about speech balloons. Connector tools does entirely different thing from speech balloons.

@theoz: Cool use of the feature, wouldn't have thought of this!

Yeah, that's a neat trick!

theozh, while searching for something else, I came across this video of Jabier's about what I think is a new LPE that's not in Inkscape yet:

https://www.youtube.com/watch?v=lOWTeZC_LjM

@brynn, thanks for that hint. It's the LPE "transform by 2 points" and it is at least in Inkscape 0.92.0.
It's an interesting feature for path transformations but as far as I experienced the path does not keep "sticking" to the other object(s), whereas the LPE "Attach Path" does.