Q: Syncing

Sync is only oneway, from PC to your device. Unless you have the music on your PC, iTunes is going to wipe out what you have on your device if you are syncing to a new library.

You can only transfer Purchased music over to Itunes on your PC.

iTunes Store: Transferring purchases from your iOS device or iPod to a computer

http://support.apple.com/kb/HT1848

As for you own music, you may have to use a third party software to copy over. A good Free one is called Sharepod which you can download from Download.com here:

http://download.cnet.com/SharePod/3000-2141_4-10794489.html?tag=mncol;2

Kind of.... here's how it goes. You need to "authorize" that computer to your iTunes account. http://support.apple.com/kb/HT1420

Then when you sync it, it will keep all of your photos and apps. But your music will be erased. You'll need to use your new computer iTunes to re-download all of the music you purchased from iTunes for free . http://support.apple.com/kb/HT2519. Then you can sync again and you're set.

If your music on your phone that you used another computer to put on there WASN'T bought in iTunes then you'll need to go back to that old computer and buy iTunes Match for $25/year so that you can re-download that music on your new computer. http://support.apple.com/kb/HT4914.

  And if your music on your phone that you used another computer to put on there WASN'T bought in iTunes and you can't access your old computer.... then yeah you're kind of SOL.

Hope this helps!

This is not true. Apple has homesharing to transfer all of your music. No need to buy anything out. See response below.