Is it possible rip game resources from a .smc file? Specifically art, music, sprites, etc. How does an emulator copy the system it emulates?
It's possible, in the sense that the information is all there in some manner. But an smc file is basically a compiled program with embedded resources, and there isn't even a standard compiler or standard format for storing the resources that you can start from.
And as far as image data goes, there is a good chance it will be in the palettized and tiled format used by the PPU, although it's also not unlikely that it will be compressed in some manner or another. But the palette will probably be almost impossible to find by static analysis, and the tile maps are probably generated from the level data rather than being explicitly stored anywhere. You may have better luck running it in an emulator and extracting the data from VRAM.
For music, the situation is even more discouraging. SNES audio is most akin to a MOD file: instruments are sampled, and then the individual samples are pitch-adjusted and mixed to generate the output sound. The SNES provides hardware to decode the instrument samples, manipulate the pitch, and mix them together, but no high-level program (i.e. no equivalent of a mod file "tracker") to play back actual songs. So you may be able to find the BRR-encoded instrument samples in the same manner you may be able to find the image tile data, but the song data can and will be formatted completely differently in different games. Again, your best luck may come from extracting the state of the APU as an SPC file and working with that.
As for your other question, see How do emulators work and how are they written? for a previous answer on that very topic.