All 3rd party apps should be in your iTunes library on your computer, and would be if you had Sync Apps selected under the Apps tab for your iPhone sync preferences with iTunes from the start. With this selected, you can install apps and remove apps from your iPhone via the iTunes sync process. After installed an app direct with your iPhone, the app will be copied to your iTunes library automatically the first time you sync your iPhone with iTunes after doing so.
Or at iTunes > Preferences under the Store tab, select Music, Apps, Books. After downloading an app with your iPhone, the app will be downloaded by iTunes on your computer automatically.
With your iPhone connected to iTunes, at the iTunes menu bar go to File and select Transfer Purchases From - the name of your iPhone.
After confirming all apps on your iPhone are now in your iTunes library, select Sync Apps under the Apps tab for your iPhone sync preferences with iTunes making sure all apps on your iPhone are selected below followed by selecting Apply.
There are two way to transfer songs. One is by selecting Sync Music under the Music tab for your iPhone sync preferences with iTunes selecting the iTunes playlists, artists, genres, etc. you want transferred to your iPhone followed by selecting Apply and a Sync.
Did you sync the phone with a different computer in the past? Is the computer you are using now Authorized to the same iTunes account that you have on the iPhone? Is all of the music on the iPhone purchased from iTunes?
If the last 2 of these are true, connect the phone, but do not sync. Choose "Transfer Purchases" from the iTunes File menu.
Once that is done click on the phone's name in the left pane, then on the Music tab in the right pane, and select the music from your iTunes library that you want on the phone.
Now would also be a good time to read the manual, as all of this is explained in detail in it. YOu can read it on the phone with Safari (there is a built in bookmark for it), or download it at: http://manuals.info.apple.com/en_US/ipad_2_user_guide.pdf