color mode and color profile in Id

Color management in InDesign, Illustrator, and Acrobat should be set up in Photoshop > Edit > Color Settings. Then, use Bridge > Edit > Color Settings to synchronize the decisions you make in Photoshop color management over to InDesign, Illustrator, and Acrobat.

My favorite settings are Adobe RGB (1998), for anything RGB, and Coated GRACOL for anything that is strictly CMYK printing press. I also choose GRACOL for Gray, and I leave Spot alone. Then, I find it is useful to set Color Management Policies to "Convert to Working ..." for all three: RGB, CMYK, and Gray. This enforces workflow color management sameness. Finally, I turn off all three Ask Me switches, just because I don't want to answer the same question over and over in a dialog box. Just do it, I say. I leave the rest of the Color Settings dialog box at default values for Conversion Options and Advanced Controls. To complete your holistic color management, click Save... and give your color management method a name. Ok. Ok again. Now it is off to Adobe Bridge > Edit > Color Settings. Choose the same custom-named color management settings. Ok. This silently reaches out to InDesign, Illustrator, and Acrobat and changes their color management settings to be the same as what you decided in Photoshop. Now all 4 are synchronized. Check them to be sure. It doesn't hurt to pick your custom-named .CSF color settings file directly in InDesign, Illustrator, and Acrobat. 

Now you can effectively stop worrying about color profiles. New documents merely need to be set to either RGB or CMYK color mode / transparency blend mode. Nowadays, I work RGB fully, and convert to CMYK printing press only at the moment of exporting a PDF where I choose the commercial-printery-recommended color profile (there can be exceptions to that in specific printing scenarios).

Since you are designing an EPUB, you would likely choose RGB color mode in Photoshop, Illustrator, and RGB transparency blendmode in InDesign. You only consider the sRGB outcome at the moment you export the EPUB. That is done automatically. When exporting PDF, you would choose your output color space destination, which could be RGB for online viewing or a specific CMYK printing colorspace for a physically-printed job.

Approached this way, for most projects, you get to stop micro-managing the color translation process that is handled by the behind-the-scenes Adobe Color Engine, aka ACE. Focus instead on good design and better workflow techniques.

Hi @Hosun26059267k946 , InDesign doesn’t have a single document color space like Illustrator and Photoshop—you can mix CMYK, RGB, Lab defined colors in the same document. InDesign lets you assign both an RGB and CMYK profile to the document—see Edit>Assign Profiles..., and it includes a Transparency Blend Space to handle mixed color modes when the spread has transparency

You can set an Intent from the Document Setup as @Rene Andritsch suggests, but all that does is set the default Swatches and the Transparency Blend Space to either RGB or CMYK—once you set the Intent, you can still create new swatches in any color space or change the blend space. Here the Intent is RGB, but I have a mix of CMYK, Lab, and RGB fills on the page:

As a summary, can I understand that color profile determines/influences color mode?

InDesign document has an RGB and CMYK profile assignment—the RGB assignment handles the color managed preview of document RGB colors and swatches, and the CMYK assignment handles document CMYK colors and swatches. You can see that in my mixed color example—if I change the RGB assignment it affects the RGB fill, but not the CMYK and Lab fills:

When creating a new document in InDesign you can choose your output intent as Print, Web or Mobile. This will also set your document colors. For web documents all the colors in the Swatches Panel will be RBG and with print documents your colors will be CMYK by default.

 If you want to change it after you created the document go to the menu “File > Document Setup”, the color Settings can be found in the menu “Edit > Color Settings”

Also the Transparency flattening will use the respective color space. If you want to keep all color settings consistent across your apps use Adobe Bridges function (Edit > Color Settings or CMD/CTRL + K) to set them for all your apps at once.