Hi Carsten, I'd like to give you a slightly different viewpoint on the answers to some of your questions that may help you understand better. As DB said, I hope you like reading!
CarstenDierks said:
For me it is difficult to understand why gravitational waves (gravitons) should propagate through spacetime with c and, thus, cause space curvature (if I have understood that correctly).
This is the first part of the problem right here. Gravity
can propagate in waves, but the normal everyday gravity that we deal with does not. It is merely a distortion of spacetime.
Think of an electron. There it sits. It has an electric charge, which distorts space all around it; we call this distortion the "electric field." Its nature is described by Maxwell's equations. But do you see any waves coming from it? No, you do not. If you did, then it would be emitting energy- and a motionless electron has no energy to emit, so that would violate mass-energy conservation.
That field, in quantum mechanical terms, is a field of
virtual photons. These virtual photons are emitted and reabsorbed by the vacuum surrounding the electron so quickly that their presence is not in violation of the conservation law, because of uncertainty. Remember, though, that these are
virtual photons, not
real ones.
OK, so now we move the electron around some way. In fact, we oscillate it.
Now it has some energy; and it emits that energy- as photons! And these are not virtual photons- they are
real, and they go shooting off into space. In fact, if we get a whole bunch of electrons to do this together, inside of a wire, we can make
radio waves. And in fact, that is exactly how a radio works- and it makes electromagnetic energy, which is photons.
So now you can see the difference between an
electric field and an
electric wave. The first is
virtual photons; the second is
real photons.
In the same way, a planet or star creates a distortion of space around it; but instead of being the space of electrical fields, this is the space of gravity fields. And that space, instead of being a separate entity from our normal spacetime like the space of electromagnetic fields,
is our normal spacetime. So there are a few things that are a little different because of that. But the principle remains the same.
Now you can see that gravity waves are a different thing from the gravity field; and you can also see that the gravity field is only virtual gravitons (yes, yes, I know, we haven't proven they exist yet... I'm getting there), but the gravity
waves are
real gravitons. They make up
gravity radiation.
So now your question is, "what is the speed of gravity waves?" And the answer is, "the speed of light." And your next question (and it is a different one!) is, "what is the speed of propagation of gravity?" And the answer is the same.
Now, all we have right now to describe gravity is the equivalent of Maxwell's equations, called the General Theory of Relativity, but for gravity instead of for electromagnetism and light. This theory talks about a lot of other things than gravity, because gravity warps spacetime, and GRT tells all about spacetime; but among the things we get from GRT is the field equations for the gravity force, and for gravity radiation.
We have QED (quantum electrodynamics) for our quantum theory of light and electromagnetism; and we even have a quantum
field theory to describe electromagnetism and light. But we have neither a quantum theory nor a quantum field theory for gravity. Every time we try to make one, we run up against infinities in all the equations. There's some really crucial concept we just don't understand yet.
But that doesn't mean we don't understand gravity; we have field equations for it. We just don't understand
quantum gravity. Keep in mind that all of electronics up until a very short time ago were all based completely on Maxwell's Equations; we never needed QED to design electrical circuits. Just recently, we started doing things sophisticated enough that the field equations aren't enough; but we still don't do very many things like that, and mostly we still just use the field equations. There are actually electrical engineers who are having problems because they have to learn quantum mechanics- QED, specifically- and they have only ever needed Maxwell's equations all their lives!
CarstenDierks said:
(1) If gravitons (gravitational waves) are not at rest in a gravitational field, this would imply to me that mass needs to constantly emit gravitational waves (gravitons) to "replace" those which are "gone".
No. They are
virtual gravitons. They are emitted and reabsorbed by the vacuum, because it is under stress from the presence of the mass. Just as it is under stress from the presence of an electric charge and emits and reabsorbs virtual photons.
CarstenDierks said:
(2) If mass curves spacetime: Is the curvature once "engraved" in spacetime and "rests" there until a new gravitational wave "updates the information"?
The curvature changes as the object moves, but the change reaches out across the curvature at the speed of light. So there is a lag at the outside reaches of the gravity field. But remember, the waves are created by oscillation; simple movement doesn't distort things enough to create gravity waves.
CarstenDierks said:
Or:
(3) Is the curvature of spacetime just "newly" evoked by every ripple of a gravitational wave passing by?
I assume this is obvious from the above.
CarstenDierks said:
(4) Do gravitational waves interfere with each other? Probably yes because gravitational forces and the curvature of space of two objects do add up.
Yes, of course they would. But remember that you would have to either reflect them from something, or you would have to have two sources of waves; simple gravity fields aren't enough to create waves, you have to have oscillation.
CarstenDierks said:
(5) Is it allowed to conclude out of (4) and (1) that the path of gravitons is not straight but also influenced by the curvature of spacetime (of other objects)? Meaning: Gravitons (gravitational waves) have to travel along our (curved) cosmos as it exists?
Yes, that is correct.
CarstenDierks said:
(6) Out of (4): What about gravitational forces of 2 objects of identical mass on a 3rd object right in-between the two? Is the gravitational force for the 3rd object zero? But is spacetime not curved at that point due to the sum of the curvature of the first two objects?
There will be an area where the curvature of space-time forms a "lane" directly between the two massive objects. Any object along that lane, and equidistant from the two massive objects, would feel no net force. But don't be fooled by your physics book's picture of a "rubber sheet" with the two massive objects making "dimples" that both attract the object between; this is in four dimensional spacetime, so it is just a matter of the forces balancing.
Keep in mind as well that such an object would still be subject to
tidal forces, unless it were of zero thickness. So it's really best to say it feels no net attractive force, because it
does feel a tidal force that is the sum of the two tidal forces, rather than their difference (I'll leave it to you to figure out why; it will give you confidence in dealing with such situations).
CarstenDierks said:
(7) Out of (6): So are gravitons (gravitational waves) and the curvature of spacetime really equal?
No.
Real gravitons are a sign of gravitational
waves;
virtual gravitons are a sign of a gravitational
field.
CarstenDierks said:
(8) Out of (2): Is this true for black holes? Do they curve spacetime and the curvature "rests" there because the gravitons (gravitational waves) cannot escape from inside of the black hole? Is the gravitational field of black holes never "updated" by gravitons (gravitational waves)?
Yes, this is also true of black holes. The gravitational
field does not emanate from inside the hole, nor do the virtual gravitons; the field is the
consequence of the mass, not the
product of the mass, although you will come across books by some rather famous people who have forgotten this. Similarly, the virtual gravitons are not emitted by the hole; they are produced by the vacuum as a result of the stress placed on it by the warping that is the consequence of the mass, they are not produced by the hole. For the rest, including the lag, everything stays pretty much the same. I did another post in which I described frame dragging, and there are some consequences that you should think about of that that I did not detail in that post. Can you see what they might be?
CarstenDierks said:
(9) Out of (1), (3), (4), (7) and (8): How can black holes capture gravitons (gravitational waves) inside the Schwarzschild radius and, at the same time, emit gravitons (gravitational waves) to curve space and exert gravitational force?
It is two different things. Remember, it is not the singularity that emits the virtual gravitons; it is the vacuum that does it. That should clarify this point for you. In field terms, the curvature of spacetime is controlled by the mass inside it; there is no reason why that curvature should not continue right on through the event horizon, although we cannot look inside the event horizon to see that it is so.
It is probable (I have not seen it mentioned anywhere) that any gravity waves that might be emitted by the singularity would not be able to exit the event horizon, because gravitational radiation could not make it past it any more than light could.
CarstenDierks said:
(10) Out of (9): How does quantum and/or string theory explain the speed and escape speed of gravitons (gravitational waves)?
I think the above is sufficient; remember that there is no viable quantum theory of gravity, and that string theory cannot currently provide specific equations that describe this state of affairs. I'd stick with the field equations that we have that we know work; they are our best source of knowledge at this time.
CarstenDierks said:
I hope I was able to put everything into the context as it currently occurs to me - and to show where my gaps in understand (relating) it are situated.
Carsten
Well, I hope that helped!
DB, I also hope I didn't irritate you- my intent was not to replace or refute what you were saying, it was to add my own perspective, which seems different from yours, though not in opposition to it. I expect to learn a thing or two from reading your responses.
the second a star is formed in space it deformes (curves) spacetime fabric, and by doing so it effects spacetime by sending gravitational waves along space forever. Once the star is formed and balanced in space, it's job is done, and space has adapted to the deformation of this new star. So the star is the rock, the gravitational waves are the ripples and spacetime fabric is the water. So gravitational waves are not constantly emited, it happens once and travels as a wave at the speed of light. Those which are "gone" have already done their job of curving space. They will keeping doing their job forever, but always at further and futher parts of the cosmos. It is now space curvature (created by the wave) to do it's job of creating and exerting gravity. (Think of gravitational waves through the water anology, but don't think of it as what gravity is, because you can't sink to the bottom of spacetime. The bowling ball anology is good for gravity.)
If two bowling balls were put on the sheet, there would be a "groove" running between them. This is what I meant by a "lane." 
