Q: How do I add the songs from my iPod to my list of songs on iTunes without losing any?

If I sync them it seems like the songs on my iPod will be replaced with only the songs from iTunes. How do I do this?

Yes, that's what will happen...  Ideally, all songs on your iPod are already in your iTunes library.  AND you keep a backup of that iTunes library, and restore from that backup if your computer fails.  An iPod should not be the only place with a copy of your songs.

iTunes syncing is generally in one direction only, from the computer's iTunes library to the iPod.  You cannot use iTunes to transfer song files from iPod to computer (except for songs purchased from the iTunes Store).  However, there are third-party methods and utilities that can transfer from iPod to computer.  If you do an Internet search on something like "ipod transfer," you should get some links, including a CNET article on the topic.

Depending on the method used, if some songs are BOTH on the iPod AND in your iTunes library, you may have to go through the "consolidated" library and remove duplicates manually.  Going forward, you can use this method to back up your computer's complete iTunes library (not just your songs) to an external drive

Back up your iTunes library by copying it to an external drive - Apple Support