Will the App be synched when I connect my new iPod on my Mac ? Do I have to do something special before selling my old iPod ?
At the very least, make sure you sync your old one to your Mac before you sell it. When you sync, it should copy purchased items from your iPod to your Mac.
If you have time, back up your iPod: Connect it to iTunes, then right-click (or control-click) and select Back Up. You can then restore your new iPod from that backup. This will restore your mail accounts, sync settings and app data to the new iPod. It will not restore the correct locations of your apps or home screen folder contents.