I understand that JPEG is a lossy compression standard, and that the 'quality' factor controls the degree of compression and thus the amount of data loss.
But when the quality number is set to 100, is the resulting jpeg lossless?
Jpeg is lossy regardless of the setting. At 100, you just get the LEAST loss possible.
It's easy enough to test. Whip up a simple .bmp, compress that to a q=100 jpeg, then re-extract back to a .bmp. Use Gimp/Photoshop to do a "difference" of the two bitmaps, and you'll see the lossiness - it'll be much less noticeable than on a q=50 or q=1 conversion, but still be present.