This is a very specialized question about color management. I'd suggest you'll get more response either in the Photoshop forum
or the Color Management forum
Moving the discussion to Photoshop General Discussion forum.
your hardware-profiled (device-specific) monitor profile should always be highlighted in System Preferences> Displays> Color: Display Profile — never set your monitor profile to device-independent profiles like sRGB, AdobeRGB
forget anything to do with 1.8 Mac legacy gamma...profile your monitor to something like 6000 kelvin, D60, 2.2 gamma, luminance 120 cdm2
for the Web, always Edit> Convert to sRGB (if not already there), then File> Save for Web & Devices — include the sRGB ICC profile or not (i usually strip the profile for the Web)
Photoshop already displays sRGB 'accurately' so i wouldn't get too caught up in second guessing that for Web publishing
here is some reading
basic theory (Photoshop color management)
save for web (see profiles in action)
5 simple steps to profile enlightenment (assign or convert profiles)
Photoshop Manages Colors print workflow (Source> Print Profile)
when you come back, i will recommend you only discuss one point at a time and include screenshots...
The second post said that this was a very specialized question about color management.
No, it is not. It is another example of someone who does not know the first thing about color management, i e device dependence.