I don't know if you can check or set the WAAS channel number directly (and I couldn't find anything about it in the C172 G1000 manual) but even if you can there's really no point. When you load the approach, the G1000 gets the WAAS channel number from the database as part of the general approach definition and configures everything automatically.
I heard or read somewhere that the original concept was that pilots would 'tune' the WAAS channel in the same way that they tune an ILS frequency, but that idea was dropped because an RNAV approach is totally dependent on the database anyway: if you trust the G1000 to load all the waypoints, altitudes and other information correctly from the database then there's no reason to think it will load the wrong WAAS channel.
As for your specific questions:
(1) How may I know which approach I am able to shoot?
You read your G1000 manual, check the approach database, and review the approach plates to make sure that the approach is available and you meet all the requirements. If the approach is in the database that doesn't automatically mean that you can fly it, there can also be climb performance or altimeter setting requirements (for example) that are unrelated to the G1000.
(2) Is the WAAS channel number automatically selected when I load the corresponding flight plan in G1000?
Yes. The G1000 sets up the approach completely for you, the only input required (usually!) is to load the approach and select how you initiate it, i.e. via an IAF or radar vectors.
(3) [Can I] get the LPV glide path guidance without loading any particular approach (set the WAAS CH number for instance?)?
No, this wouldn't make any sense. The LPV glideslope is constructed virtually by the G1000 for each approach and the WAAS input just provides correction to an existing GPS position, it doesn't give you a position directly. So even if you could receive the WAAS corrections directly (and maybe you can, for all I know), the G1000 wouldn't be able to generate a glideslope without all the other approach information about the runway, elevation etc. It would be like asking, "the magnetic declination here is 4°W, what's the correct magnetic heading to fly from A to B?" Unless you know the uncorrected heading, the correction by itself isn't useful.