Good question.
From what I've read, the Yabause Wii app is at an extremely early stage. Saturn emulation is not particularly well-developed in general, and I think that getting it to run acceptably on the Wii is even harder. The wiki page says that some games run at 5-10 fps, which is promising from a technical point of view but not so much from the point of view of someone who actually wants to play Saturn games on the Wii. Check out the
Yabause site for more info, I suppose. Also, given your assessment of Yabause's performance on your presumably fairly powerful PC, how effectively do you think the humble Wii can run the same program?
As regards the loading method, the Wii cannot read CDs, as far as I know. From the looks of things, at the moment the program only supports loading roms from SD, but if the project sees significant development you can be sure that they will implement stuff like DVD and USB loading in future.
To get it to run, download the file from the wiibrew wiki page and follow the instructions there. Alternatively, you can download it via the homebrew browser app directly onto your SD card in your Wii. You don't need Linux.
In short, it's not very good if you want high-fidelity Saturn emulation.
As regards SSF, if it is open source, then it is in theory portable to the Wii, as is any emulator. However, the power of the Wii plays a large factor in whether it can actually run effectively or not. If it's not open source, then no port.