Many thanks go to you Ron P., walt.farrell, and v_kyr for your useful help.
I presented two questions.
The first question was about the Affinity Photo Color Preferences settings for the RGB Color Profile and the 32bit RGB Color Profile. I still to not know what the Affinity Photo programs does. Does it use the Windows 10 default setting which might be different from the original windows setting because the computer display was calibrated? Or, if a default computer display profile setting cannot be found, will the Affinity Photo program use the color profile defined with the Color Preferences setting? Or, no matter the system color profile settings, will the Affinity Photo program use the color profile defined with the Color Preferences setting? My guess is the last alternative is what the Affinity Photo program does. This would mean that I should change the "sRGB IEC61966-2.1" to be "SAMSUNG_L_FL156FL05_C01_D65_201801171412.icm" which is my current color profile because the display has been calibrated. In either case, I am still dealing with the RGB color space.
The second question was about telling the program to "Embed ICC Profile" when exporting JPG files.
I have experimently determined how this works. The Embed ICC Profile function has nothing to do with the Affinity Photo Color Preferences settings. In all cases, if the Embed ICC profile entry is not checked, no profile will be included with the exported JPG file. If the Export the ICC Profile: phrase is "Use document profile" and the Embed ICC profile entry is checked, the "sRGB IEC61966-2.1" profile will be included with the JPG file. On the other hand, if the ICC Profile: phrase is a specific profile name provided in the pull down list, that color profile will be embedded with the JPG file when the Embed ICC profile entry is checked. In other words, an ICC profile might or might not be included with the exported file, and, if a specific profile is required to be included with the exported file, that profile can be defined with the pull down list. The "document profile" (the default) for export is the "sRGB IEC61966-2.1" profile. I would either include the default document profile or not include any profile. I cannot see a reason to include my personal monitor color profile with a file. Not knowing how other systems would present my image, the conservative decision would be to include the default color profile with the file. In any case the file size difference is not be very great when the color profile is included with the file.
If you would like to add to or clarify what I have written above, please do so.