The participating/non-participating lists are a good place to start. In general, you can expect that agencies on the "participating" list will have everything, including comments, though how far back they go will vary. Which agencies fall into which categories is determined partially by statute and subsequent executive order, and, for those agencies not required to participate, by agency preference (I discussed the specifics a bit more in a blog post). For the FCC in particular, as you know, you're fortunate in that comment data is available in at least a semi-sane format from the FCC itself, via ECFS.
As to your other question, about the laws that authorize rulemakings, that turns out to be a giant can of worms, but one I'm super-interested in. The short answer is that regulations.gov alone probably won't be able to answer that question for you in its entirety, but you can probably get closer in combination with other sources. There are a few different paths:
- Authority references will be included in the text of the rule, sometimes as a separate Authority section (particularly for final rules), and sometimes as a note at the end of a section. You're more likely to be able to identify these if you examine the HTML representation of the document from federalregister.gov than the plain-text representation you get from regulations.gov's API, so that's probably a good starting place. You can cross-walk from one to the other via the federal register number often included with a rule on regulations.gov. (Side-note: regulations.gov now uses this nicer HTML for regulations.gov display purposes, as of just recently, though they don't yet make it available via the API; I expect this will be rectified soon-ish).
- Separate authority metadata is available for rules that meet a high enough threshold of significance for them to be subject to review by OIRA. If that happens, there will be additional structured data about authority. Again, federalregister.gov is the best bet, and they pull these OIRA authorities out as separate metadata fields.
- Once a rule has been codified into the Code of Federal Regulations, you can trace authority from the CFR back to the US Code via the Parallel table of Authorities and Rules (PTAR); Sunlight has at least a first pass at a parser for it if you want it structured. This source is much messier than the others, though... probably best as a last resort.
So... no simple answer, but hopefully that's a start. (Also, I almost recommended that you look at Dokket for more info about the FCC, before I realized who had asked this question.)