I have found no reference for this specific symbol in the context of flow charts, but let me make some educated guesses:
- Is parallel mode = parallel process?
Most probably yes, for the simple fact there is no alternative directly provided in "draw.io" in the Flowchart category.
- Is this the shape I wanna use for my use case?
You did not describe your use case very clearly.
If you want your diagrams strictly follow ISO5807, you may need to eliminate the diamonds from the symbol (which can be done in draw.io). But maybe this is not really important for your case? Ultimately, it depends on the audience and if you can make sure they understand what you are trying to express with the diagram.
- Does it mean something different?
No (see 1.)
- What are those diamonds for?
- Do they represent nested routines?
I have no idea, but does it really matter? Maybe they are just intended for making the symbol less ambiguos, since unconnected parallel lines could be sometimes misinterpreted as something else (edges, two separate symbols, annotations). Maybe they were just inspired by the usual diamond symbol in flowchart for decisions, which describes a non-parallel branch.
So I would recommend to use it if one has an audience which can ask the author directly in case they have doubts, or when a legend is provided, or when it is pretty clear from the context. Otherwise, better strip the diamonds out of the symbol, so you can make your diagram following ISO 5807 strictly.