1) It totally depends on the modem hardware and the software installed on the modem. Every manufacturer does this differently.
If you get ssh
access, work your way through the file system; usually there's a place were skeletons of the web-pages you see are stored, and from these you can sometimes work out how to access this information. But often it's not obvious, and needs a bit of perseverance.
2) It's totally possible; personally, I only know modems (Fritzboxes) which do have SNR bins.
What happens in your modem is that there is a second, dedicated CPU (often a DSP variety) that runs the signal processing necessary for DSL communication. Depending on how the signal-processing software works, it can communicate a lot of information about the signal, or little.