Can I burn songs on a disk and then transfer to iTunes?

As seeing that I'm having no luck with trying to sync my songs on iTunes with my iPod, and I've looked at 3rd Party sites but they only do a few songs and it's not ALL the songs I want. I've tried many different ideas especially a few with the ones that people have told me on this forum. But, it didn't work. And I'm getting really angry that nothing is working. So, here's 2 new question:

1) If I were to burn all the songs on both iPods to disks, and delete all the songs on both playlists, would I be able to transfer the songs from the disks back on to iTunes?

2) If nothing works, do you think it would be better to send it to Apple to get fixed? From what the woman from Apple told me that I have no music in my playlists, except for the music that iTunes puts there. I know many times that before this all happened, iTunes kept telling me to backup my songs and I didn't do that. I would like to either put all the music on disks or put them on a hard drive and then transfer them back to iTunes, but I'm not sure how.

Can anyone help me with these 2 questions? I'm sick of listening to the same songs while I'm in my car, and I want to sync them so that they change, and shuffle doesn't do anything. I had it set up by songs played. Which means that after a song plays, it goes to the bottom of the list and the next song becomes the first song. In this case it isn't. I'm afraid that I've spent so much money on songs, and now both iPods might be ruined and there might be songs that I can't buy again. So, I'm in desperate need for help and it doesn't seem like anyone knows how to deal with this.

Thanks,

Raven