Your iTunes Media folder, where all the song files are stored, may be on your external drive. However, the iTunes Library file, which is a database of all of your songs with supporting data, such as song file location, playlists, playcounts, ratings, etc. is located in your computer's Music/iTunes/ folder. Therefore, if you did not have a backup of you computer's main storage disk (the one with the system), that file would be lost if the computer or hard drive died. On the new computer, you are essentially starting your iTunes library "from scratch" and adding all of your songs from the external drive.
You cannot transfer your playlists from iPod to computer using iTunes. There are third-party methods and utilities that can transfer songs from iPod to computer, but they may or may not transfer playlists. If you do a Google search on something like "ipod transfer," you should get some links.
I did use a transfer utility a few years ago, that had the feature to transfer playlists. This is that product (Music Liberator)
I never had to use the playlist transfer feature. Other utilities may also transfer playlists. There is a free trial, so you may want to give it a try to see if it does what you need.