a.) What is the actual difference of version 2 and 3? I mean, version 2 seems easier because I don't need all those cables for the RRC-1258. Additionally, when travelling I only have to bring the K3/0. The laptop will have to run with TeamViewer anyway, because I still want to see the waterfall and I have to control the PA and the antenna. So, can someone tell me the actual advantage of the use with RemoteRig? Is it faster with RemoteRig?
The following is based on reading more than actual experience.
For someone who is just focused on the control side, the difference between 2) and 3) is that you have to choose whichever one matches the setup on the remote radio side.
For someone who is assembling both the remote and control side, I believe it's a more individualized decision.
When working remote, sound quality and latency are probably the biggest practical concerns. That should cause someone to be biased towards a solution that provides the best quality/least latency...and I would expect that having devices that are focused on one particular task would tend to provide the best performance. At a minimum, relying on a computer to relay audio exposes you to the potential for unexpected latency or glitches, processing power, and/or network interface is needed for other applications (say, like running Teamviewer or generating a waterfall display).
Personally, I might be tempted to try starting out without the RemoteRig devices for simplicity, and see if it was good enough for my needs. However, someone did recently share with me a set of block diagrams, showing the evolution of a particular remoted contest station. They choose to use RR-1258's, and I'd bet that it works better. (Whether it's enough of an improvement to justify the cost would depend on the need.)
I imagine that it's possible to wire the remote-side up for both standalone and RR-1258 use, but I suspect that there would need to be some experimentation done on how to change the audio paths for the different configurations. I think you should probably seek to choose one way or the other.