Some files are naming some other copyrights and authors. If you need, check them all in the latest SVN.
VideoLAN produces free software projects under the GNU General Public License, version 2 or any later version. The License is under the COPYING file of the SVN and all the tarballs.
The source code for VLC media player is released under version 2 of the GPL, thought binaries may be released under version 3 if required by included libraries. For more information, see this press release.
You can use any GPL software without any restriction.
However, most MPEG codec are patented in some country and require payment of royalties for any use. It's the responsibility of the user to do so if based in such country.
Redistribution / Copying
You can redistribute, copy and modify any GPL software, including VideoLAN's, but you have to conform to the LICENSE, which is mainly that you have to provide the source code and use a LICENSE compatible with the GPL. If you don't understand, please check this article about GPL on Wikipedia.
Names / Trademark
The official name of the project is VideoLAN.
The official name of VLC is VLC media player. It used to be called VideoLAN Client, but this is not true anymore.
VLC is the familiar name of VLC media player.
The soppera-cone is the official icon of the program.
The official names of VLS are VLS and VideoLAN Server.