If the music is out of copyright, or if you own the cppyright to the music, you can upload as much of it as you want. If the music in question is under copyright, and you don’t own the copyright, the basic answer is: never.
And i’m not sure what you mean by “a special site with no downloads.” Once you make copyrighted works available on the internet, you are violating the law.
IIRC, if you’re found liable for copyright infringement, the damages can be severe ($750 and up per copyrighted work). You can still be found liable if you gave the work away for free, and the copyright holder does not need to prove that the infringement caused actual (financial) harm.
Not quite. If you the music is under copyright, and you don’t own the copyright, the basic answer is actually, “Only with permission of the copyright holder.” Such permission is routinely granted by some artists, usually under permissive licences such as the Creative Commons ones.
The OP might not even be aware that he has permission, since he may have never bothered to read the licence that came with the music, or perhaps never obtained a copy of the licence through the distribution channel. There’s a great deal of Free (as in free to redistribute) music out there, some of it by fairly established artists. If he’s got anything by, say, Jonathan Coulton in his collection, chances are he’s got permission to upload it to his website or most anywhere else, provided the artist is properly credited.
In most cases they get away with it simply because the copyright owners aren’t aware of the infringement. If and when they do, the video containing the unauthorized music will be muted or removed entirely. (This happens fairly often.) The uploader may also be subject to a lawsuit, though I don’t know if this has actually happened to any YouTube users.
Odds are you don’t have any music that is of expired copyright. Even if the copyright on the song was expired (70 years after author’s deaths), the recording/performance is still protected. So you’re limited to recordings of yourself singing or playing “mary had a little lamb” or “Twinkle Twinkle little star”
Unless you’re working for a band/music, and it’s your job to do so, you probably shouldn’t be worrying about how to upload music that isn’t your own. In an ideal world you’d give people the name of a song and the artist and they would legally obtain a copy (purchase) or preview at the record store.
One reason is that the volume of YouTube members is so large that it’s difficult for the copyright holders to police what is being uploaded. Some copyright holders might tolerate use of their songs on YouTube because it’s free publicity (think of the viral video of the dancing bridal party).