I think I misunderstood a bit. The YUM file from the adobe site basically contains a repository definition file that, when installed, can let you install flash from the fedora program called "yum." In short, it does not contain the flash program itself. So you should be able to doubleclick this file and it should install the definitions for you. Now you need to invoke "yum" (as root) to actually install flash. If you see "waiting for other processes to finish" just try waiting a few minutes.
When I said before to log in as root, I was referring to the command line. There isn't a way to graphically log in as root. (As far as I can tell Fedora doesn't allow this anymore and this isn't unique to live systems). What you need to do is open up a command line and type
You won't be prompted for a password since you're on a live system. Now type on the command line
Code:
yum install flash-plugin
And it should find and download the appropriate package. You might as well get wine while you're at it (yum install wine).
IF that doesn't work then try going back to the download site and get the linux tar.gz file. Save this to your home folder. Now open up a command prompt and invoke the following:
Code:
tar -xzf install_flash_player_10_linux.tar.gz
(unzips archive)
Code:
cd install_flash_player_10_linux
(change directory the folder that just got created)
Code:
chmod +x flash_player_installer
(makes the file execuatble, that is, let's you run it like a 'program', if you're really curious try looking up chmod on Wikipedia)
Now do su - to log in as root, and then change directory to your home folder (cd /home/<your.user.name>/install_flash_player_10_linux).
Code:
./flashplayer-installer
(don't forget the dot slash in front)
Then just follow the instructions. When asked for an installation path, try /usr/lib/mozilla and see if that works.
But Drakeo is right, you will need external programs to play mp3/wmv and such, as Fedora can't include support for that due to patent restrictions in USA. You will need some binary packages for programs like MPlayer or Xine. Since you're using a live USB system, building apps from source probably isn't a good idea; the compilers and libraries will quickly fill your drive, and the large number of read/write cycles on compilation will quickly wear it out. You might have a look at
http://rpmfusion.org/ for this and read some of their tutorials.