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Photoshop and Illustrator paragraph and character styles are quite basic.
InDesign has a lot more features.
Probably why the character and paragraph styles don't work - they have different features than that are available in Photoshop and Illustrator - so they're not compatible.
Probably same with colour swatches. InDesign can have mixed swatches and colour modes. Illustrator and Photoshop cannot.
That is your Illustrator file is either CMYK or RGB - same with Photoshop.
Where InDesign al
Where InDesign allows multiple colour spaces in the same file.
Just hazarding a guess. But that's my logic here at the moment. I'm sure there's more to it.