1 - basic PC or Mac based profiling only sets grey scale / white point. It has no control over Gamut. Brightness should be set manually. So no, it doesn't set colour space. See my post on ICC profiles.
2 - LightSpace builds LUT for full display calibration, but only if the display or system in use can work with LUTs. Most displays can't. See Penta Monitors for ones that can as an example.
3 - Monitors can only ever be calibrated to specification below their own maximum capabilities - very, very few displays can do P3, and none can do XYZ (but XYZ is NOT a display colour space as such - it is based on P3)
4 - The underlying screen defines all capabilities - colour space and dynamic range. This can't be improved other than by building a better display screen. Bit depth only changes the 'steps' between the min and max a given screen can work with - exactly as you say.
5 - normal TV definitions define what we work with in post - what you can see at home has to define the displays used in post-production. It's no good having a huge range that can be seen in post, as it will never look right when broadcast. If home TV change spec from SMPTE/Rec709 then post can change too...
6 - The pre-sets in AE and PhotoShop (ICC profiles) are not guaranteed accurate, and use the ICC concept of source and target profiles in partnership. Thsi is very different to the LUT based workflow we use in the broadcast and film industry - again see my post on ICC profiles.I have never found the pre-sets to be accurate enough.
Hope this helps.
Mob Boss at Light Illusion