-There is no "iPod Classic 30GB", but there is a 30GB model of the 3rd, 4th (Photo/color display version) and 5th/5.5 gen iPods.
-You can replace the battery on either of these models, but you have to buy the right battery, depending on if you have a 3rd, 4th, or 5th gen iPod. You can find these all over the place online, but in my experience the batteries on Amazon and eBay are of extremely poor quality.
-I used to repair iPods and have come across issues where it won't shut off/go to sleep. I've noticed that sometimes if the hard drive is aging and is causing delays, the iPod won't go to sleep until it has finished reading the hard drive. I have a 5th gen iPod and you have to wait 10 seconds after it starts reading the hard drive before you can put it to sleep. I also have a 3rd generation iPod that won't go to sleep no matter what you do; at best, you can connect it to a wall charger, get it to say "Charging" and then unplug it, which will "put it to sleep" but the backlight will stay on. Otherwise, holding Play/Pause or selecting the "Sleep" option does nothing. Probably a motherboard issue.
-You can get either iPodLinux or Rockbox for either model of these iPods.
http://ipodlinux.sourceforge.net/index.shtml
http://www.rockbox.org/download/