Replaygain doesn't change the audio at all, it just scans each song/album, and makes them either louder or quiter, so I don't have to keep touching my volume. Nothing more. Right?

AFAIK, Replaygain is only a tag. The sourcefile is not physically altered in any other way other than adding the tag information. Hence, you also need a player which can actually read the RG tag (like Foobar does). Without a compatible player to read the tag and adjust the output volume, Replaygaining won't help you.

And the best way to scan an entire library of music is (in foobar) to "scan selection as multiple items," correct?

Yes, if the files are all tagged correctly otherwise, "Scan selection as multiple albums" will tag all of your albums with both the song gain and the album gain.

One other thing: If you use mp3gain, it will (can? This may have changed.) alter the global gain value for the file (in either the header or each frame, can't remember which), so that ANY mp3 decoder would output the correct volume. Problem was, you could only get either the song gain or the album gain, not both. Another problem was that if you didn't keep the log, you couldn't reverse the changes. I think that the newest version of mp3gain saves the changes as ape tags.