The signals stored in the file should be the same, but the container is different and Brainstorm would allow completely different things with each file.
The "source" version (option 2) might not be handled correctly in many processes. It is therefore not recommended, and is going to be removed from the interface at some point.
In general, do not use anything in Brainstorm that is "not recommended" unless you know exactly what you are doing or that you want to reproduce older results that used the deprecated function.
4. Finally, by using "Simulate"->"Full Source Maps From Scouts", what do we exactly obtain? The same that in point "1"?
No. You get the signals or 2) and 3), copied back into a full cortex file. If a scout includes 200 vertices, its time series would be replicated for each of the 200 vertices (= copied to the 200 corresponding rows in ImageGridAmp).
You mean that Brainstorm can't manage "Source" files for connectivity, right?
The connectivity functions handle source files correctly, but not these hacky source files generated with the process "Downsample to atlas".
If you use scouts, it means that you are interested in only e.g. 68 ROI time series, and not the full 15000 source time series. Therefore, you should run your connectivity analyses on these 68 signals, instead of reconstructing and artificial file with 15000 signals, that would later be shrunk again to 68.