I believe mp4 is the extension used by both AAC and Apple Lossless.
Obviously lossless is far superior to any lossy codec, I use flac almost exclusively and I swear to you, with good speakers, the difference is obvious. But back to topic:
AAC can also be lossless and lossy. So take it for what it's worth. I've heard such rumors that AAC lossy is better than mp3, but they are both lossy...... eck.
What can and cannot be used to burn audio CDs depends on your burning software and plugins installed. For example, FLAC (one of the lossless formats) has a plugin that allows Nero to make audio CDs from FLAC files.
AFAIK, Nero supports .mp4 natively, but I do not believe Window's built-in music CD burning capability does. For data CDs, of course, anything goes.
Regarding size - it depends on format, of course, but generally lossless averages around 50% of the wav source. IE., a 'full' audio CD that would rip to wav at 700mb will end up ~350mb of lossless compression (depending on format used, type of music on the CD, etc). So...yeah, they are huge compared to mp3 compression. And, realistically, 90% of the people out there can't tell the difference.
Many of us can, though, and disk space is cheap enough that the space saved is not worth sacrificing the quality (IMHO).
Not all MP3 encoders are treated equal, and not all AAC encoders are treated equal. LAME, for example, fares better than Shine, Gogo, and other various under-optimized encoders.
Generally, yes, AAC achieves transparency at lower bit rates than MP3. One of the 'best' AAC encoders has actually been developed by Nero and is still under development.
Use lossless whenever you possibly can, but if there are space constraints, or if you're not listening on fairly high end equipment, don't be too fearful of either MP3 or AAC. But, again, use lossless whenever you can. wavPack and FLAC are popular encoders (wavPack also has a very cool hybrid mode), but ALAC is also fine, albeit slower, less effective and less versatile.