How to extend the standard color picker to pick and edit HEX colors? In Ask Different there are similar threads (e.g. Choosing hexadecimal web colours), but unfortunately no one is resolutive for me.

The perfect solution would be Hex Color Picker (a plugin for the standard picker), because it goes beyond picking allowing to edit/create swatches also. Unfortunately, it does not work for me: for some reason the hex picker returns wrong hex values. E.g. a full red image (#ff0000) created in photoshop, is evaluated as #f70016 (see image below). I tested this behaviour picking both from Photoshop and from an exported .png opened in browser. Both in Maverick and Mountain Lion.

Can you suggest me an alternative solution or a fix for this issue?
Test it and you'll see that Photoshop is guilty for not rendering in the same color space. 

You need to change the color profile of your image in photoshop.