I can only speak to the Vivaldi stack. I have heard the Rossini and it is very good but I have never compared it to the Vivaldi in my system. I started with the Vivaldi DAC and was very impressed. I added the Upsampler mainly for it’s streaming capabilities but soon found that its upsampling and multiple filter choices made a substantial improvement, especially in the current V2 software. I next added the external clock and for me the improvement was noticeable but not as big a difference as the Upsampler. YMMV as others have claimed more substantial improvements.
So to directly answer your questions I would say the external clock will make a difference for the DAC for all sources, not just streaming. But it may be subtle, so you should try to audition one before buying. Most dealers stock them, so it’s easy to try.
The dCS Bridge is for DACs that don’t have inboard streaming capability and would not be needed in the case of the Rossini.